







Shaking hands at a party 
20141203 

From Nazrul: At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Please help me. Answered by Penny Nom. 





4 card hands 
20141102 

From Ronaldo: How many Mus hands (combination of 4 cards allowing repetitions)
can be made from a deck containing 8 types of cards?
RRRR, RRRC, RRRS, RRR7, RRR6, RRR5, RRR4, RRRA,
RRCC, RRCS, RRC7, RRC^, RRC5, RRC4, RRCA,
RRSS, RRS7, etc.
I think 330. If so, what is the formula? Answered by Penny Nom. 





A lost combination 
20140928 

From Kim: I cannot remember my combo to this simple lockbox. It is 3 digits from 09. They can be used more than once . I thought it was 117..but no joy. I am fairly sure it was using those digits 1, and 7. can you give me a list of all possible combinations, using 1s and 7s, for the 3 number code? Thank you and I am in awe of people who have math skills, for I certainly do not. Answered by Penny Nom. 





Selecting a meal at a school cafeteria 
20140718 

From Gil: A school cafeteria offers 2 main entrees, 3 fruits, 4 vegetables, and 3 drinks. If a plate consists of 1 entree, 2 vegetables, 1 fruit, and 1 drink, how many different plates can a cafeteria manager make? Please explain how you derived at answer. Thank you Answered by Penny Nom. 





6 character strings using 1, 5 and 9 
20140615 

From Kevin: How many 6 digit combinations (i.e., 159159) can be made from 3 different numbers (i.e., 1,5, and 9)? The numbers will obviously have to repeat. A link to a calculator that could list all the combinations would be helpful. I've come across these sites: http://textmechanic.com/PermutationGenerator.html, and http://textmechanic.com/CombinationGenerator.html , but am not sure how to use them for my specific case. Thanks. Answered by Penny Nom. 





Three digit padlock combinations 
20140320 

From Edwin: Would appreciate if you can provide me with the list of different combinations that can be obtained from a three digits number. I lost the access code of a three digits number padlock (and need to open it order to get important documents Answered by Penny Nom. 





Some 3digit combinations 
20140223 

From ivana: How many possible 3digit combinations can be made of the numbers 123456?
None of the numbers can repeat in one combination. I used to know a formula but have been out of school for some time and cannot remember. Answered by Penny Nom. 





8 numbers from 80 
20130904 

From susan: Out of 80 numbers how many combinations of 8 are there and what are they. Answered by Penny Nom. 





Four digit combinations starting with 7 6 
20130515 

From Kaye: How do I find the rest of a four digit combination starting with 7 6? Answered by Penny Nom. 





Sixdigit passwords 
20130319 

From Judy: Hello:
Can you please explain why the answer to the following question is 10^6?
What is the number of possible sixdigit passwords when using the digits 0 through 9, with repetition allowed.
Thank you. Answered by Penny Nom. 





Four digit "combinations" using 0124 
20130227 

From Ayana: What are all the possible four digit combinations using 0124. Please list them for me. Thank you. Answered by Penny Nom. 





The last 4 digits of a cell phone number 
20121222 

From Jacob: If the last 4 digits of a cell phone number, XXXXXXABCD, are restricted where: A cannot be 0 or 1 and B cannot be 0 / how many possible 4 digit combinations are left? Answered by Penny Nom. 





Some 4 digit numbers 
20121025 

From samira: How many 4digit numbers are there in which the first and last digits are the same? Answered by Penny Nom. 





4 digit combinations 
20121017 

From Scott: How many different 4 number combinations from 0123456789 with 2 out of the 4 odd and 2 out of the 4 even, with no numbers repeating. Thanks Answered by p. 





A security code 
20120901 

From Breanna: The code is made up of five two digit numbers from 01 to 20 entered in a certain order. How many different security codes are possible with this system Answered by Penny Nom. 





Golf for 16 in 7 rounds 
20120816 

From Elizabeth: Hello,
I am trying to sort out golfing for 16 guys for 7 rounds. However the twist is that the teams are broken down into 8 old boys vs. 8 young boys. Ideally, each of the players would only play each other once within their own team and then twice within all of the matches. Is that possible? Thanks for your help, my brain is hurting! Answered by Victoria West. 





6/49 
20120525 

From Mark: Can you explain why the lotto 6/49 (a lottery of 49 numbers and 6 slots) is a combination and not a permutation?
It seems to me that it would a permutation given that the numbers are written in numeric "order" when you look them up in the newspaper.
I realize that 49P6 is orders of magnitude larger than 49C6. But I am confused about the reasoning behind it. Answered by Robert Dawson. 





A lost combination 
20120306 

From pam: I lost the combination for my luggage that I haven't used for many years. It is a 3 digit combination. I'm pretty sure only these numbers could have been used: 0,1,2,3,7,8,9. Can you give me a calculated list of all these combinations? Answered by Penny Nom. 





Four digit combinations from 1,2, ..., 9 
20120226 

From Errol: show me a list with all four digit combination numbers from 0 9 Answered by Penny Nom. 





A combination lock 
20111221 

From Sheila: I have a combination lock with a total of 3 rows of single digits 1  9.
In order to open the lock, the numbers chosen for each row together
add to 12.I'm looking to generate a list of numbers that I can
sequentially try so that I can open the lock. Answered by Robert Dawson. 





The total number of roles that a user can be assigned 
20111202 

From Colin: Hi, I want to define an equation for calculating the total combination of roles that a user can be assign in a system.
Here is the background: There are two types of roles that a user can be assigned. These are object roles and data roles. There must be at least 1 object and 1 data role in the system. A user must be assigned at least 1 object role and at least 1 data role. A user can be assigned as many object roles and data roles as are created in the system. There is no upper limit to the number of roles that a user can be assigned except for the total number of object roles and data roles that exist. The number of object roles and data roles in the system are independent.
Can someone please assist? Thanks. Answered by Penny Nom. 





In how many ways can 12 members of volleyball team line up ... 
20111118 

From Aatir: In how many ways can 12 members of volleyball team line up if the captain and assistant captain have to remain together. Answered by Penny Nom and Stephen La Rocque. 





The number of People who Know Each Other 
20111021 

From Ted: I'm trying to prove that at a party
where there are at least two people,
there are two people who know the
same number of other people there. Answered by Robert Dawson and Penny Nom. 





3digit, daily numbers 
20110929 

From Margaret: I need the list/group for a raffle that would contain the combinations
for a 3 digit (000999) daily number. There would be 100 tickets sold
with 10 3digit numbers from each numerical group beginning
from 000's, 100's 200's, 300's,...900's. No duplicates/replacement. What would be the
list of possible combinations of each group of 100 tickets, keeping each
different group/list of combinations in separate blocks of 100 tickets
without duplication. So I could use 1 list of 100 this year and the next list of
combos next year and so forth. Please help!
Example: 000,197,245,367,445,569,618,777,842,964
What would be the possible lists of each 100 tickets?
Thank you Answered by Penny Nom. 





5 crayons 
20110917 

From John: How many four color combinations are possible with 5 crayons Answered by Penny Nom. 





58 choose 4 
20110826 

From Jean: Using only the numbers 159, how many times would the
number 23 appear in combinations of 5 numbers?
... Can a list be provided as well?
Thank you very much,
Jean Answered by Penny Nom. 





5 digit numbers using the digits 5 and 2 
20110427 

From sissy: I need a list of all possible 5 digit combinations using 5 and 2 numbers can repeat Answered by Penny Nom. 





Is this a permutation or a combination? 
20110111 

From Lamont: If I have 10 marbles: 3 blue, 2 yellow, 1 purple, and 4 red
How many ways can I pull out 3 different sets of marbles?
Is this a permutation or a combination? Answered by Penny Nom. 





A punchcode lock box 
20101129 

From Doug: I am a real estate agent that uses punchcode lock boxes on houses to store the keys. I need to crack the code on one of our boxes, so I need a list of the possible combinations.
Rules:
4 digit code
Numbers 09
Each number can only be used once
Order of the numbers does not matter.
With advice from this site, I have calculated that there should be 210 possibilities.
10x9x8x7 (5040) gives me the total number possibilities and 4x3x2x1 (24) gives me the total number of ways to arrange those numbers.
So if I divide the possibilities by the arrangement, I get 210. (5040 / 24 = 210) GREAT!!!
Now, how do I develop a list of those 210 combinations?
Thanks for your help. Answered by Robert Dawson. 





My phone is "sim locked" 
20100610 

From Daniel: Question from daniel:
got a phone that says sim locked, it requires 09 digit code to get in, how many combinations could there be if you could please list the possibilities, the number can be repeated. Answered by Penny Nom. 





Six numbers from 1 to 20 
20100510 

From martine: how many different combinations can be made from numbers 1 to 20 using them only once in a six number scale Answered by Penny Nom. 





6 items are taken 3 at a time 
20100412 

From Kristen: Explain the three different scenarios that could occur and would result in the following number of outcomes when 6 items are taken 3 at a time. Give reallife examples.
a. 63 = 6 x 6 x 6 = 216 possibilities
b. 6! / (6  3)! = 6 x 5 x 4 = 120 possibilities
c. 6! / (6  3)! 3! = 20 possibilities Answered by Tyler Wood. 





4 books at the book fair 
20100411 

From Erin: You have enough money to buy 4 books at the book fair. There are 6 books to choose from. How many different combinations are there. Answered by Tyler Wood. 





How many 5 card hands in a deck of 52 have 2 aces and 3 other cards? 
20100323 

From Travis: How many 5 card hands in a deck of 52 have 2 aces and 3 other cards? Answered by Penny Nom. 





Selecting 3 students from 16 
20100309 

From amper: A class has 12 boys and 4 girls. If three students are selected at random from the class,
what is the probability that they are all boys? Answered by Penny Nom. 





How many triangles...? 
20100222 

From deciree: Given 12 points, no 3 of them on a line with 6 red, 4 blue and 2 green points.
a) How many triangles have vertices all the same color?
b)How many triangles have vertices with each vertex a different color?
c)How many triangles have at least one green vertex?
thanks to lorraine! Answered by Penny Nom. 





A student wants to take four courses 
20100221 

From deciree: A student wants to take four courses. She has 11 courses to choose from: 6 sophomore level and 5 freshmen level.
Each course is available at 8,9,10,11 am.
a)if the student wants to take 2 freshmen and 2 sophomore courses, how many choices she have?
b)If she wants to alternate these courses, freshmen,sophomore,freshmen,sophomore, how many choices does she have? Answered by Lorraine Dame. 





A pushbutton padlock 
20100117 

From Vince: Hi,
I have a pushbutton padlock using ten buttons (1234567890).
Five digits must be pushed in order to open the lock.
Each digit can only be used once.
Order is not supposed to matter.
How many different possible combinations? And what are they? Answered by Harley Weston. 





A set of 5 numbers 
20100110 

From Marco: I need to generate in an Excel or other table all possible combinations for a set of 5 numbers with the following criteria:
1. Numbers can repeat.
2. Order does not matter.
3. Numbers may be from 09
4. The sum of all numbers is equal or less than 31.
5. The sum of all numbers is equal or greater than 10.
6. One of the numbers is 2.
7. One of the numbers is 5.
8. One of the numbers is 7.
Marco Answered by Penny Nom. 





Two digit numbers 
20091210 

From Jim: Can you tell me how many 2 digit numbers can be created
from the following:
1118539 Answered by Penny Nom. 





Sixletter words 
20091124 

From christine: How many sixletter words (not necessarily an English words) are there in which exactly three of the letters are z's? Answered by Claude Tardif. 





6 numbers from 53 numbers 
20091117 

From MIGUEL: IM A STUDENT IN HIGH SCHOOL AND IM HELPING THE SOCCER COACH WITH PLAYS
SO I NEED ALL THE POSSIBLE NUMBER COMBINATIONS OF NUMBERS 1 53 IN SETS OF SIX
THE NUMBER CAN ONLY BE USED ONCE IN EACH SET. Answered by Penny Nom. 





6 numbers from 12 
20091114 

From david: how many combinations of 6 numbers can there be using 12 different
numbers without using the same numbers more than once?
2, 3, 5, 8, 9, 11, 12, 14, 17, 19, 20 & 31. Answered by Penny Nom. 





Pennies, nickels and dimes 
20090922 

From Kiadadh: Show 12 ways to come up with 28 cents using only pennies, nickles and dimes Answered by Robert Dawson. 





4 number combinations 
20090910 

From jeremy: Here's my question...
I've been playing the lottery, I know what a waste of time. I would like to know how many 4 number combinations can be derived from a set of 10 numbers, when no number can be repeated in the present string of 4 numbers being selected. Answered by Robert Dawson and Harley Weston. 





Combinations 
20090831 

From Joe: I'm trying to find out how many combinations are possible out of 18 using only 4 numbers, but with no repetition of a single number in the 4 number sequence. EX: 2,3,2,5 wont work. Is it possible to create a list, and if so did my calculator lie to me when i got 70 as an answer? Answered by Penny Nom. 





Unlocking my suitcase 
20090821 

From Jamboree: I need to have all the possible combination of three digit between 09, i have seen the answer that there are 720 combination are there. Could you please show me all those combination numbers so that i could try it out to unlock my suitcase, will you please write it down all those combination and send it to me Answered by Victoria West. 





Passwords 
20090708 

From Tim: pretend I have a password that is  9k7d4112p5o
assuming that you continuously guessed wrong until that exact
combination was the only possible answer left;
how many times would you have to guess?
capital letters are not relevant
and you do not know how many digits there are Answered by Stephen La Rocque. 





Selecting 3 people from 4 
20090602 

From muhammadibeaheem: Use mathematical induction to prove that for all integers n≥1,
is divisible by 3.
Question 2;
A club consists of four members.How many sample points are in the sample space when three officers; president, secretary and treasurer, are to be chosen? Answered by Penny Nom. 





7 digit combinations 
20090511 

From CAROL: I NEED TO KNOW HOW MANY 7 DIGIT COMBINATIONS FROM 09 THERE ARE WITHOUT ANY REPEATES,
OR WHAT THOSE COMBINATIONS ARE? Answered by Penny Nom. 





Combinations and permutations 
20090507 

From Renee: We are trying to figure out the equation or how to solve the problem of how many combinations of 4 digits you can get out of 09 without repeating the numbers in a set (i.e., no 0001, 0002) begining with 0123, 0124, 0125 etc
Thanks! Answered by Stephen La Rocque. 





Permutations 
20090430 

From Evan: There are 24 possible combinations of the numbers 1 through 4, and 5 times that many
combinations of the numbers 1 through 5. Are there 144 (6x24) possible combinations of 1 through
6? Or is it 6x5x24? Is there a formula for determining this?
Thanks,
Evan Answered by Penny Nom. 





Fourdigit combinations 
20090418 

From Carri: How many 4digit combinations can be made out of digits 1, 2, 3, 4, & 5 using each number once? What are the combinations? Answered by Penny Nom. 





How many handshakes took place? 
20090415 

From wm: Suppose every member of the House of Representatives shakes
hands with every other member exactly once.
How many handshakes took place ? Answered by Penny Nom. 





Possible combinations of 2 numbers between the range 1 and 50 
20090403 

From Carl: Hi, I think I'm right in saying that there are 1225 possible combinations of 2 numbers between the range 1 and 50?
I used the function =combin(50,2) in excel to establish this.
What I'd like to do is be able to prove this using a calculator or pen and paper.
I've searched your website, but to be honest all the algebra stuff just confuses me!
Could you explain the math without using algebra please.
(We run a tote in the office, where you pick any two numbers between 1 and 50, and if your numbers come up you win, so I'm trying to work out all the possible combinations. The same number can't be used twice either)
many thanks
Carl Answered by Stephen La Rocque. 





What is the probability of accepting the box? 
20090322 

From x: a box consists of 10 light bulbs inspected by the following procedure: 2 bulbs are chosen at random without replacement. the box is only accepted if both bulbs work. suppose that the box contains 1 defective bulb. what is the probability of accepting the box? Answered by Penny Nom. 





16 golfers 
20090318 

From Bill: We have 16 golfers. We golf for 5 days, in foursomes. It should work out that each player plays with each other player 1 time exactly.
I just can't figure it out.
Thank you in advance!
Bill Answered by Claude Tardif and Victoria West. 





License plates and poker hands 
20090314 

From CC: You have a license plate it can have 6 numbers/letters you can use the numerals 09 and the letters AZ how many combos are possible and how did you figure it out?
Question 2,
Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards. Answered by Harley Weston. 





15 flavors of ice cream 
20090311 

From Pedro: I was given this word question an was somewhat confused can u help me understand.
An ice cream vendor sells 15 flavors of ice cream and u want to sample at least
4 different types. how many different combinations of ice cream would u be able
to sample? Answered by Penny Nom. 





Trifecta 
20090309 

From Annie: I want to know how many combinations are there for the first 3 horses in
a race of 20 horses. For example, the horses can come in 1, 5, 7 or
7, 5, 1 which are totally different combos. I've only found formulas
where the 1, 2, 3 and 3, 2, 1 are counted as the same combo.
In horse racing every combo is different.
Thank you. Answered by Penny Nom. 





Three number combinations 
20090227 

From mark: How many three number combinations can I get using 1,2,3,4,5? I can use a number more than once. Answered by Robert Dawson. 





Combinations of 11 from 13 
20090217 

From john: i would like to know the possible combinations of eleven folds form 13,
i think they are 78 lines in total, thank you Answered by Robert Dawson. 





4 digit arrangements of 7 3 6 6 
20090205 

From Carole: I need all the four digit combinations using the numbers 7 3 6 6 Answered by Penny Nom. 





Missing three digits in a phone number 
20090130 

From Elmer: I have part of a phone number. the first 3 digits are 212, the last digit is four, and the three missing digits are all odd, how many numbers will I have to call to get the right number?
212 _ _ _ 4? Answered by Stephen La Rocque and Penny Nom. 





How many color combinations are possible for the four rooms. 
20090126 

From Irfan: John wants to paint 4 rooms in his house, each a different color and he may choose from 7 different colors of paint.
How many color combination are possible for the four rooms. Answered by Robert Dawson. 





5 "digit" combinations 
20090122 

From Timothy: I was wondering how many different 5 digit combinations are possible using 09 and az and you can use the same letter or number repeatedly in the combination. Answered by Penny Nom. 





I lost the combo to my lock box 
20090110 

From Rob: I lost the combo to my lock box, I remember 2 of the #'s in the combo are 6, but dont remember which ones.
What are the possible scenarios knowing the above? Thanks! Answered by Stephen La Rocque. 





Permutations and combinations 
20081228 

From KHADIJA: What's the difference between Permutation and Combination? Answered by Penny Nom. 





Dividing some flowers 
20081209 

From gaurav: two girls have picked 10 roses,14 daffodils,15 sunflowers . what is the number of ways they can divide flower amongst themselves? Answered by Stephen La Rocque. 





License plates 
20081117 

From Clayton: Okay, so in this situation a license plate must have four letters (AZ) and four numbers (09), ex. ABCD1234, where repeating a letter or number is allowed ex. AAAA1234, or ABCD1111, or AAAA1111. The order of letters first numbers second, or number first, letters second is allowable, and each state has its own plates, so ABCD1234 from New York, and ABCD1234 from Minnesota are considered different combinations, how many different license plates could there be? Answered by Penny Nom. 





Three digit combinations 
20081112 

From Jimmy: How many 3 digit combinations are possible using numbers 19?
How did you get that answer? Answered by Harley Weston. 





4 digit combinations 
20081105 

From Laura: I need to know all the number combinations possible with a 4 digit combination with double zero in the middle??? Answered by Penny Nom. 





A three 09 tumbler lock 
20080922 

From Louis: I recently gave my daughter an old briefcase which uses a three 09 tumbler lock. She set the lock and now she can’t open one side.
Q. Is there a 3 digit combination number generator available to give me the 1000 possibilities?
Thanks,
Lou
PS In this type of lock you can repeat the same digit three times. Answered by Penny Nom. 





Mixing watercolour paints 
20080907 

From bob: So, I'm making a chart to help me mix watercolor paints. There are
25 different paints. Each paint will mix with another paint just 1 time.
There is no need to mix red with blue, and then blue with red. Since
the result is the same, we only need 1 combination of the 2 paints.
And there is no need to mix red with red, so we can eliminate 25
combinations of the same paint. Answered by Penny Nom. 





Three letter combinations 
20080815 

From Shelbie: How many 3 letter combinations are possible, if you can repeat each letter?
I learned an easy way to do this in school, but fail to remeber what that was... Answered by Penny Nom. 





Choosing 5 numbers from 39 
20080804 

From robert: Hi,
I am sending you the web page where I found the question of 39 numbers and =
5 choices, please see below.
How does they comes up with the 120 combinations?
How can I comes up with the 120 combinations in a printout form?
Please read all the way to the bottom of there example and see where they talks about the 120 combinations. Answered by Victoria West and Harley Weston. 





3 digit combinatios from 09 
20080727 

From Mike: I need to know all the possible 3 digit combinations using the numbers 09.
The numbers can be repeated as long as they are not of the same set.
Example for not repeating: 123 is ok but not 321 or 231,132,213, etc.
Please help me. Thanks, Mike. Answered by Stephen La Rocque. 





Choosing 4 numbers from 70 numbers 
20080721 

From Jeannine: When using numbers from 1 to 70 in sets of 4, how many combinations are there without having the same combination twice?
Thanks Answered by Penny Nom. 





Choosing 5 numbers out of 39 numbers 
20080718 

From robert: Please list the way I can choose 5 numbers out of 39 numbers, without repeating them, starting at number 1.
Please send me a list of all 120 combination. Answered by Harley Weston. 





Making Change 
20080709 

From Peter: In how many ways can you make 30 cents with quarters, nickels, and pennies? Answered by Penny. 





Probability and two digit numbers 
20080707 

From Peter: What is the probability that if you multiply two randomly selected two digit whole numbers, the result is greater that 100 and less than 200. Express your answer as a common fraction. Answered by Janice Cotcher. 





6 things from 45 things 
20080508 

From Hakan: Hi im a student studying advanced mathematics and i would like to know how many
possible sequences of six digits there are using the numbers from 1 to 45 (1 & 45 are
included) but none of the sequences can be identical even if the numbers are in
different orders.
Example : 1,2,3,4,5,6
2,3,4,5,6,1 these two sequences are identical even though the digits have
changed their order so therefore is incorrect.
I would like to know the easiest way to write these sequences along with how
many there are. This is extremely important for my year 12 exams Thank You. Answered by Penny Nom. 





Twenty golfers 
20080316 

From john: I have a group of 20 golfers. We plan on playing 6 rounds of golf in 4 days. I would like to have the most possible combinations of players without each player playing with anyone if possible, in the 4 days of golf Answered by Victoria West. 





3 numbers from 14 numbers 
20080304 

From Jackie: I would like to know all the combinations possible with 3 numbers in each
combination, using the numbers 114. Answered by Penny Nom. 





Choosing 5 numbers from 56 numbers 
20080302 

From alexavier: need all of the 5 digit combinations using the numbers 156. Answered by Harley Weston. 





How many different hamburgers is it possible to order? 
20080217 

From Elizabeth: At a hamburger stand you can order a hamburger with any of the following, in any combination: ketchup, mustard, pickles, onions, tomatoes, mayonnaise and/or lettuce. How many different hamburgers is it possible to order? Answered by Penny Nom. 





Five digit combinations 
20080215 

From Debbie: I would like to get a list of all the possible 5 digit combinations of the numbers 12345. Answered by Penny Nom. 





A briefcase lock 
20080211 

From Alfred: A briefcase lock has 3 columns of numbers each 09. It opens with the correct combination of three numbers.
How many combinations are possible to open the lock. Answered by Penny Nom. 





Choosing 6 numbers from 42 
20080119 

From Marcus: If i have 42 numbers to choose from and i could only choose 6 numbers at a time without choosing the same number twice in the same row, how many possibilities are there? Answered by Penny Nom. 





Combinations of the numbers 1 to 22 
20080117 

From Frank: How many combinations are there for 22 numbers (1 to 22) of 4 numbers and 5 numbers. For 4 would it be 22 x22 x22 22 for 4 one more x 22 for 5? Thank You! Answered by Penny Nom. 





Five boys and two girls in a line 
20080112 

From pankaj: There are 5 boys and 2 girls.In how many ways can they stand in row so that no two girls are together? Answered by Penny Nom. 





Unique combinations of 5 names 
20080108 

From tony: Hi  I have went through so many of your answers and can't find exactly what I need. I am looking to find all possible combinations of names programmatically.
Example:
If I have 5 names:
Mike
Tony
Joe
Bill
Bob
How many unique combinations can I put together (regardless of order)
For instance:
(Mike, Tony) is 1 combination
(Mike, Joe, Bob) is another combination
but (Tony, Mike) is the same as (Mike, Tony) so it would not be valid.
I am pretty good in logic and math but by no means an expert. I am a programmer and am looking to store each unique combination in a database (I will handle that part of course I just need help on the unique combinations) Answered by Victoria West. 





Combinations 
20080108 

From david: is there a simple formula to follow for the number of combinations a set of numbers could have
ie.( lotto 649, 6 numbers, 149 range) Answered by Penny Nom. 





3 digit numbers made from 1,2,3,0 
20080107 

From cheri: COULD YOU GIVE ME ALL THE # COMBINATIONS I NEED 3 DIGIT NUMBERS MADE OUT OF THE NUMBERS 1, 2, 3, 0.. I CAN ONLY COME UP WITH.. IM TRYING TO MAKE PASSWORDS FOR MY FINGERPRINT LOCK I PURCHASED, AND THEY TOLD ME THERE I COULD GET 78 DIFF COMBOS,,,,, PLEASE HELP ASAP, NEED TO GET MY CUSTOMERS HOOKED UP SO THAT THEY CAN ENTER THE CLUB HELP AND THANK YOU SO SO MUCH Answered by Victoria West. 





A 5 button lock 
20080102 

From mandy: i have a problem. I have a 5 button lock.and i seem to have forgotten
the combination. You can only push each button once but you can push
more than one button at a time and you don't have to use each button
but i am pretty sure i used all five. for example it can be
1,2,3,4,5 or 1,2&3,4,5. I was wondering if anyone can get me a list of
all the possibilities because i really need to get the box open. Answered by Penny Nom. 





Bingo cards 
20071230 

From Martin: I'm trying to produce bingo cards.
There are only 4 numbers on each bingo card.
The numbers are between 1 and 12.
How do i produce as many bingo cards as possible without duplicating number combinations? Answered by Victoria West. 





Combinations of 1, 2, 3 
20071229 

From gary: I can only write the numbers 1, 2, 3, in six different combinations. Are there any more possibilities Answered by Penny Nom. 





How many triangles can be formed? 
20071221 

From pankaj: Q.There is 2 lines parallel to each other. If 1st has 5 points in it and 2nd 3 points in it,how many triangles can be formed? Answered by Penny Nom. 





12 balls are divided between 2 boys 
20071120 

From anita: In how many ways can 12 balls be divided between 2 boys, one receiving 5 and the other 7 balls ? Answered by Penny Nom. 





A 3 digit lock 
20071106 

From Michael: We have a 3 digit lock that only allows for 5 possible numbers to be used. (The numbers can repeat) What are the total number of combinations that can be created. Answered by Penny Nom. 





How many combinations can there be for 12 games? 
20071101 

From Melissa: I am looking to find out how many different combinations there are in 12
sports games. Let's say I have 12 baseball games, total 24 teams, and
there can only be two results, win or lose, no ties. How many
combinations can there be for 12 games? Thankyou very much. Answered by Penny Nom. 





Combinations and horse races 
20071028 

From Ian: How do I calculate the number of combinations for:
Horse races,1 horse in each race.I want all combinations covered.
e.g.5 races, 1 horse in each race. R 1&2, R 1&3,R 1&4, R 2,3,4,5, R 1,2,3,4,5 etc etc.I have worked it out manually to 27 combinations
but if I want to cover more than 5 it will be a big excercise to work out the cost manually.
Many Thanks Answered by Victoria West. 





Some four digit combinations 
20071025 

From Larisa: Please tell me the answer or how to get the answer of every possible digit combination of 5173, for instance1735, 1753, 1573, 1537, 1357, 1375, etc. Answered by Stephen La Rocque. 





Choosing 3 crayons from 6 crayons 
20071023 

From Greg: I have six crayons: red, orange, yellow, green, blue, and purple. I need to know how many combinations of three crayons can I have. Answered by Penny Nom and Melanie Tyrer. 





2 password policies 
20071017 

From Larry: 2 password policies are in question.
Policy 1 states that a password must be between 6 and 8 characters
Policy 2 states that that a password must be exactly 8 characters.
Both policies state that Passwords can contain AZ az 09 (26*2)+ 10 characters to choose from.
Which policy is stronger?
How many potential passwords exist for policy 1 and how many for policy 2? Answered by Penny Nom. 





Golf pairings 
20071002 

From Mike: Regarding arranging golf players so no person plays with anyone more than once.
You have given examples for 16 and 24 players. If it can be done, i need a
solution for 20 players, 4 players per team one round per day for 5 days Answered by Victoria West. 





4 number combinations 
20071001 

From Steve: How many 4 number combinations are possible with a total of 24 numbers. No two
numbers can be in the same group twice. Is there a matrix I can set up to get all the
combinations?
Thanks Answered by Victoria West. 





Choosing 3 numbers from 36 
20070921 

From Jon: How many distinct combinations can be made when choosing 3 numbers from 36?
IE you can only choose each number once Answered by Victoria West. 





Combinations of 4 letters from 8 letters 
20070904 

From Heidi: how many different combinations of 4 letters can be made from a set of 8 letters? Answered by Harley Weston. 





Four digit combinations 
20070904 

From Natalie: Using The Numbers 7 4 5
How many different 4digit combinations are possible, you can use any of the numbers twice. Answered by Penny Nom. 





Arrangements of children by age 
20070902 

From shani: How many different arrangements of children by age can there be in families with four children?(hint: Boygirlboygirl is different from boygirlgirlboy. Presume there are no twins)
The hint is more confusing than the question. Answered by Penny Nom. 





Rearranging the alphabet 
20070818 

From samhita: Find the number of ways of arranging 26 letters in the English alphabet in a row such that there are exactly 5 letters between x and y. Answered by Stephen La Rocque and Penny Nom. 





6 digit combinations 
20070816 

From steve: how many 6 digit combinations are there (using a number only once) are there using numbers 116 Answered by Penny Nom. 





An old bike lock 
20070808 

From Jeremy: I have an old bike lock i found in the garage of the house i just moved in to. It has four columns and the nubers are 1 through 6. I understand that there are 1236 (6x6x6x6) possibilities. Is there a graph of all the possible combinations cuz i looked all over the web and couldn't find one. Answered by Penny Nom. 





4 digit number combinations that start with the digit 2 
20070805 

From tonnie: my question is what are all the 4 digit number combinations that start with the number 2? Answered by Harley Weston. 





Permutations and combinations 
20070729 

From Marcy: I'm having difficulty teaching my students when to use permutations or combinations. Is there a "catchy" way to teach them that will help them to identify when to use permutations and combinations? Answered by Penny Nom. 





Why are these two questions different? 
20070721 

From Mac: Basically i like to know the difference between two solutions.
( I taken this questions from a web link)
Questions1) From 6 boys and 4 girls, 5 are to be selected to admission for a particular
house. In how many ways can this be done if there must be exactly 2 girls.
sol)
C(4,2)= 6
C(6,3)= 20
solutions is : 6*20= 120.
Question2) Out of 10 consonants and 4 vowels how many words can be formed each
containing 6 consonants and 3 vowels.
sol) C(10,6)
C(4,3)
and then 9! for arranging the selected words(9 character word).
solution= C(10,6) * C(4,3) * 9! = 30,48,19,200
Now my question is, why are we multiplying 9! in the second problem
and why we didnt multiply 5! in the first question ? Answered by Claude Tardif and Harley Weston. 





I need all the possible 4 digit combinations... 
20070718 

From Jo: I have lost the code for my car stereo. I need all the possible 4 digit combinations using the numerals 1 2 3 4 5 and 6. Thank you Answered by Penny Nom. 





Five button push lock 
20070706 

From Jeffrey: We have a 5 button push lock and we were wondering how many different codes were possible in this situation. In this lock each button can only be pressed once (ie it's not a numbered key pad) and order matters. How would we find out the # of possible codes? Answered by Stephen La Rocque. 





All 4 digit combinations for numbers 0 through 9 
20070621 

From Jessica: How can I find all 4 digit combinations for numbers 0 through 9? Answered by Penny Nom. 





A 5 digit key 
20070531 

From Michael: I have a 5 digit key pad lock on my truck.
I want to print out all of the combinations to try.
pad one=0 pad two =1 pad three=2 pad four=3 pad five =4.
can you help me find and print all combinations? Answered by Harley Weston. 





Specific combinations 
20070522 

From Gerald:
 I have a group of 7 men and 4 women. How many groups can be formed in which I would have: a) 3 men and 2 women and b) 5 people in which at least 3 among them would be men.
 I have a bag containing 7 black marbles and 5 white marbles. How many combinations of 5 marbles of which 3 are black and two are white are possible?
Answered by Penny Nom. 





A push button lock 
20070521 

From Werner: I have a push button lock (the numbers entered does not have a start and end i.e. 1234 = 4321 or 2341 = 3241 ...)
So if it is a 4 digit code and you have 10 buttons (0 to 9) there should be 5040 (?) possibilities and how would I list these unique combinations Answered by Penny Nom. 





All the possible 8 digit combinations of 09 
20070516 

From Christofer: What are all the possible 8 digit combinations of 09? List please
I know that there are 43046721 combinations but I want to know
what they are. Answered by Stephen La Rocque. 





How many ways can I choose 4 numbers from 10? 
20070510 

From Mitch: Can you give me a list of all possible four digit combinations using 0 to 9 no repeat numbers and the numbers do not have to be entered in a special order. If you could also show me how to calulate this it would be great Answered by Stephen La Rocque. 





Combinations 
20070509 

From Michael: Show that 5 X C(n,5) = n X C(n1,4) Answered by Stephen La Rocque. 





Probability of getting an A 
20070509 

From Christine: In a class of 15 people, exactly 3 got an A. If 2
people are randomly chosen from this class, what is the probability that
at least one of these 2 got an A? Answered by Paul Betts. 





A committee of 4 
20070509 

From Danielle: I was wondering: What is the probability that both Barb and Bob are both
on the same committee of 4 which is chosen fom their class of 10 people?
Is it 2/5? Thanks a bunch! Answered by Penny Nom. 





Lottery numbers 
20070504 

From Trish: What are all the six digit combinations between 1 & 36 Answered by Stephen La Rocque. 





Choosing 6 from a set of 12 
20070412 

From Darren: there are 12 numbers (123456789101112)
how many times can i pick 6 different numbers? Answered by Stephen La Rocque. 





Choosing numbers with no two consecutive 
20070315 

From Meghan: How many combinations are there of 3 numbers chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 but where no 2 of the 3 numbers are consecutive?
Thank you!
Meghan Answered by Penny Nom. 





How many different combinations of players can the coach make? 
20070313 

From lisa: there are 8 basketball players on a team. only 5 can play on the court at 1 time. how many different combinations of players can the coach make. the book said the ans. was 56 I do not know how that was please show me how to solve it. thanks Answered by Penny Nom. 





A survey of 9 independent questions 
20070309 

From Sueheir: I have a survey of 9 independent questions. Each of the 9 questions has the following answers (Good, average, poor) occurring equally likely. How many different combinations of answers do I have ? What is the probability of each combination? how many similar combinations do I have?... thanks a lot! Answered by Penny Nom. 





Combinations 
20070218 

From Zahid: How can i find the combinations of 5digits till 50!. Without any repeating numbers. For e.g 1,2,3,4,5 that's one 7,8,9,10,11 that another one. There might be case of getting 1,45,47,22,7 . How can i find ALL the combinations of 5digits till 50? Answered by Penny Nom. 





Four number combinations 
20070216 

From Joe: I have an uncle who plays the Massachusetts daily lottery. It a 4 number lottery. He wanted to know how many different 4 number combinations could he make using these 12 separate numbers.
3 7 4 0 6 9 1 3 7 3 9 8 Answered by Penny Nom. 





As many player combinations as possible 
20070118 

From Ken: I coach a 5th grade basketball team with 12 players. I'd like to come up with a way to get as many player combinations as possible with two teams of 6 so that the makeup of the teams is different each time. An example would be: Players 16 on one team and players 712 on the other. Then I could have 1,3,5,7,9,11 on one team and the evens on the other. Then 1,2,6,7,9,10 on one team and the rest on the other. Can you help set something like this up? Answered by Chris Fisher. 





At the ice cream parlor 
20070110 

From Bill: at the ice cream parlor, customers can chose among five different ice cream flavors and can choose either a sugar cone or a waffle cone. considering both ice cream flavor and cone type, how many distinct triplescoop with three different ice cream flavors are available? Answered by Penny Nom. 





A dozen donuts from an unlimited supply of five types of donuts 
20070107 

From Mel: how many ways can you buy a dozen donuts from an unlimited supply of five types of donuts? Answered by Penny Nom. 





How many different lineups are possible? 
20070106 

From Steve: I have 7 players on a basketball team/roster. If 5 players can play at the same time, how many different lineups are possible? Answered by Penny Nom. 





Phone number combinations 
20070104 

From Efrain: i want to know the different combinations for numbers 7 digits the number are 09 its basically the different phone number combinations example: 5556689 or 5654896 i just want to know for many different combinations are there.... Answered by Penny Nom. 





2 digit combinations 
20061204 

From Gary: please figure out for me what are the 2 digit combinations of numbers using numbers 0 thru 9 Answered by Penny Nom. 





How many licence plates are possible? 
20061124 

From Naomi: The state of New York has licence plates with five numbers followed by either a letter A or a letter B (eg. 36457A ,59972B ). How many licence plates are possible? Answered by Penny Nom. 





Show that nCr = n C(nr) 
20061122 

From Ronnie: Show that nCr = n C(nr) Answered by Penny Nom. 





How many trains of length 5 are there? 
20061120 

From Shea: A "train of length 5" is a row of blocks whose combined length is 5. Here are some examples: 122, 212, 131, 5, 14. If you use identical blocks in a different order, this is a separate train. How many trains of length 5 are there? Come up with a formula for the number of trains of length n. Answered by Penny Nom. 





Number combinations 
20061109 

From Bob: how can I find out all the different combinations for the numbers 8168 example 8168, 8868, 1688,1886,6818 etc. how many are their. Answered by Penny Nom. 





A dinner group of 16 couples 
20061102 

From Nancy: This is a realworld problem. I should know the answer but I don't. A friend is starting a dinner group of 16 couples, to be distributed across 4 houses. Each month she wants to have a different set of host houses (no problem) AND she doesn't want repeats among pairs. That is, if the Smiths and Joneses are together one month, they should not be together another month until all the combinations have been exhausted. How many valid combinations are there? Is there a formula that I can convert into a computer program? I will have to get the names from my friend and give her back the combinations as she would not be able to deal with the math formulation. Answered by Denis Hanson. 





Four digit combinations 
20061026 

From Sasha: CAN YOU LIST ALL OF THE POSSIBLE 4 DIGIT COMBINATION'S, THAT DO NOT START WITH 0? Answered by Stephen La Rocque. 





A specific 8 digit number in a 11 digit mobile phone number 
20061013 

From James: I need to know the chance of finding a specific 8 digit number in a 11 digit mobile phone number.
the number must be 29571596 and the 11 digit phone number must end in this.
All numbers 09 are used in a mobile number but the first 2 digits will always be 07.
Is there a way to work this out?? Answered by Stephen La Rocque. 





Onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5 
20061009 

From Hina: If onequarter of all 3subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m. Answered by Steve La Rocque and Claude Tardif. 





How many different threedigit numbers can you make using ... 
20060912 

From Beth: How many different threedigit numbers can you make using the numbers 2, 5, 7, 8 using the digits any number of times? Answered by Stephen La Rocque and Penny Nom. 





I have 4 numbers and want to find all possible combinations. 
20060905 

From Candace: I have 4 numbers and want to find all possible combinations. I come up with 24 but that seems too small...am I correct that there should be more? Answered by Stephen La Rocque. 





Bike combination lock 
20060716 

From Alejandra: I have a bike lock. It has three columns of the digets 19 and zero. I have forgotten the combination. Three numbers need to be imputed. What are the possible lock cominations, so that i can try to break the lock? Answered by Stephen La Rocque. 





How many arrangements are there? 
20060416 

From Jim: Can you tell me how many different combinations there are using 3 letters and 4 numbers. Letters first then numbers, example aaa0001, aaa0002, aaa0003,baa0001, baa0002, zzz9999. Answered by Stephen La Rocque. 





How to find the odds for a lottery jackpot 
20060412 

From Harvey: Is it best to use factorials to calculate the odds of winning a lottery, such as the MegaMillions that is popular in the US, or is there a better way? Answered by Stephen La Rocque. 





Probability of a committee with 3 parents and 3 teachers 
20060412 

From Javier: A committee consisting of 6 people is to be selected from 8 parents and 4 teachers. Find the probability of selecting 3 parents and 3 teachers. Answered by Stephen La Rocque. 





If you pile the 4 bricks on top of each other ... 
20060327 

From Mike: You have 4 bricks each with dimensions of 4" X 5" X 9". If you pile the 4 bricks on top of each other to form a tower how many different tower heights can be achieved? All four bricks must be used in each tower. Answered by Claude Tardif. 





Four digit numbers 
20060325 

From Kenvin: i was wondering how many possibilities is there for a four digit number with the same first two numbers and the last two is not one of the first with numbers 19 Answered by Stephen La Rocque. 





A 4digit Combination Lock 
20060309 

From Adam: I have a 4digit Combination Lock but i have forgotten the code. i do know that it is an even number, all the digits are different, the second digit is zero and the largest digit is 6. what are all the possibilities. Answered by Stephen La Rocque. 





Combinations 
20060225 

From Nancy: I NEED THE FIND THE TOTAL NUMBER OF COMBINATIONS FOR THE FOLLOWING NUMBERS IN LOTS OF 5
1,2,3,4,9,13,15,17,19,21,25,27,29,30,34,36 Answered by Stephen La Rocque. 





Teams 
20060124 

From Brianna: A small business has 8 employees. Every day, the owner designates a team to do a certain task. The owner is careful never to designate a team that is a subset of a former team or a future team, because then some people might feel not really needed in some teams. Prove that even being so considerate, the owner can choose a different team on each of 70 consecutive days. Answered by Penny Nom. 





The number of combinations of the digits 0235588 
20051207 

From Blake: If you have the digits 0235588 how many different combinations can you possibly form with these seven digits? Answered by Penny. 





5 digit numbers that include 5 and exclude 8 
20051104 

From Paul: figure out
how many 5 digit numbers are there that include the digit 5 and exclude the
digit 8.
show me how to do get to the answer. (23816) Answered by Paul Betts. 





The number of four digit combinations 
20050809 

From Kevin: My 12 year old has asked me how to figure out the number of four digit combinations possible using 0 thru 9 without repeating a number? Answered by Penny. 





In how many ways can 12 different fruits be distributed 
20050613 

From Sapta: In how many ways can 12 different fruits be distributed among 3 boys so that each receives at least 1 fruit? Answered by Claude Tardif. 





A six digit answer 
20050518 

From Angela: I have a 6 digit answer that is comprised of only 4 symbols: a square, a circle, a triangle, and an X. How many possible solutions are there and how is the best way to find out what ALL the solutions are? Answered by Penny Nom. 





A pattern of numbers 
20050421 

From Claire: We need to be able to discover the nth term in a pattern of numbers and
explain how we did it. We have arrived at the formula 1+2+3+...n=n(n+1)/2
for trios where a trio series is;
3 has the following trio (1,1,1)
4 has the following trios (2,1,1), (1,2,1), (1,1,2)
5 has the following trios (3,1,1), (1,3,1) (1,1,3) (1,2,2) (2,2,1) (2,1,2)
So the series is as follows Answered by Penny Nom. 





How many three digit numbers can I make from the four cards 
20050312 

From Sue: I have four playing cards 2,3,4,5 of hearts. How many three digit numbers can I make from the four cards. Answered by Penny Nom. 





A combination lock has 60 positions... 
20050207 

From Kathy: A combination lock has 60 positions arranged in a circle to which a pointer may be set. Three settings are required to open it and no one setting may be closer than 5 positions from the immediately preceding setting. How many different locks may be manufactured? Answered by Penny Nom. 





A seating arrangement 
20050203 

From Kay: If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Answered by Penny Nom. 





A combination question 
20050126 

From Kelly: A computer with an old processor locks up if more than 4 applications are running at the same time. If the owner has 20 applications stored in his program file, how many different sets of 4 can he run, so that his computer does not lock up? Answered by Penny Nom. 





Strings of 4 digits from 1,2,...,7 
20041209 

From Tom: How many different combinations can be made of the numbers 17 in 4 string combinations in any order? EX:7235, 3517, etc...
And if you were to include the same 2 numbers in every combination, how many would that make? EX: Using 1 & 2: 1274, 5142, 2751, etc... Answered by Penny Nom. 





Combinations 
20041209 

From Keith: i have a bucket that can hold 12(or x) number of rocks. if i have 13(or y) rocks how many different combinations of rocks can i put in the bucket without having the exact same 12(or x) rocks in the bucket. is there a formula that can be used for this problem in all cases and if so how and why does it work. Answered by Penny Nom. 





Combinations 
20041122 

From Vivek: Show that
10C0 + 10C1 + 10C2 + 10C3+.....10C10 =1024 Answered by Penny Nom. 





Visitor wins or home wins 
20040929 

From Paavn and Laddi: I have a math question i am stumped on for one of my classes. The question states that there are 14 baseball games with 2 possible outcomes for each game, visitor win or home win. How many different total combinations are possible from the 14 games? Answered by Penny Nom. 





Number combinations 
20040910 

From Angela: I need the number of possible number combinations, both 3 and 4 digit, from 059
I know that 09 has 10000 combinations for 4 digits
I also know that 09 has 1000 combinations for 3 digits
Perhaps you could explain an easier way to figure this out rather than writing all these numbers down?? Answered by Penny Nom. 





Safe cracker 
20040909 

From Adam:
Franklin's friend had taken an item from him, and put it in his family's safe, when franklin went to retrieve it he came to a combination lock on the safe, with the dial numbers going from 0 to 59. Unfortunately, he wasn't sure whether there were three or four numbers in the combination, or even which direction to turn the wheel
If it takes him 15 seconds to try a single combination, how many days will it take him to to try every possible combination? Please round to the nearest day. Answered by Penny Nom. 





Four digits 
20040710 

From Rob: I am always interested to know how the for digit works. I mean, you have correctly put it that the total numbers obtain from 0000 thru 9999 are 10,000. My question is, is there any simple formula to turn this simple 4 figures of say: 1234. Answered by Penny Nom. 





Choosing 5 numbers from 1,...,36 
20040630 

From A lottery player?: how many combinations are there for the numbers 1thru 36 when only using each number once in groups of five Answered by Penny Nom. 





Three digit combinations 
20040127 

From Kevin: how many 3 digit combinations can be made with 09. i have been told only 1,000. when i asked jeeves the response was 750 without using any digit twice. i have entered a raffle and received a ticket with 4 sets of 3 digit numbers. Answered by Penny Nom. 





Combinations of 12 numbers 
20040118 

From Cheryl: I would like to know the total possible combinations using the numbers 112. We would also like to know the formula used to calculate the number of combinations. Answered by Harley Weston. 





Six letter words 
20040117 

From Debora: An anthropologist discovers an isolated tribe whose written alphabet contains only six letters (call the letters A, B, C, D, E, and F). The tribe has a taboo against using the same letter twice in the same word. It's never done. If each different sequence of letters constitutes a different work in the language, what is the maximum number of six letter words that the language can employ? Answered by Penny Nom. 





Permutations and combinations 
20040111 

From A student: Are there more permutations than combinations for a series of 4digit numbers with the integers 09? Can you illustrate calculations? Answered by Penny Nom. 





Four digit combinations 
20031231 

From A student: i need all 4 digit combinations using 09 please Answered by Penny Nom. 





Four digit combinations 
20031202 

From Deen:
Question:
i have 3 numbers and i have to come up with all the possible 4digit combinations with those 3 numbers. Is there a formula for it?
Example:
given numbers are 129 and you need to break a 4 digit code. what are the posiible combinations that u can come up using the 3 numbers?
Answered by Penny Nom. 





Arrangements around a circular table 
20031007 

From Lori: How many arrangements can 6 people be seated round a circular table? Answered by Penny Nom. 





Four digit combinations 
20030904 

From Emma: I seriously need to find out all the four digit combinations from 0 to 9!!! My name Is Emma Dibitt and I'm going into 8th grade and I'm a student!!! Answered by Penny Nom. 





The number of three digit combinations 
20030816 

From Fred: There are four close friends having a heated discussion concerning the the number of three digit combinations using the numbers 0 through 9. The discussionÝinvolves the daily lottery.Ý Any assistance you can lend would be greatly appreciated. Answered by Penny Nom. 





Distributing r identical balls into n distinct boxes 
20030316 

From Diana: How many ways to distribute r identical balls into n distinct boxes with exactly m boxes empty? Answered by Penny Nom. 





A question on combinations 
20030306 

From Jose:
I'm an architect student and have a question on combinations. I have a grid of 3 x 3, hence a total of 9 spaces. I have 3 elements to place in this grid. How many possible ways are there of arranging this elements on this grid ? (order, orientation not important) First putting the elements each in its own space and secondly allowing the elements at a given moment to "share" one space. Since I got kind of obsessed with this I went ahead and graphically did all the combinations allowing "sharing", a grand total of 729. How could I have known this before hand ? Answered by Penny Nom and Claude Tardif. 





Mary typed a six digit number 
20030306 

From Pillar: Mary typed a six digit number, but the two 1's did not show. What appeared instead was 2002. How many different sixdigit numbers could she have typed? Answered by Penny Nom. 





The number of possible outcomes with 8 games 
20030221 

From Gianni: If 8 basketball games being played(no ties), which means a total of 16 teams, what are the total number of possible outcomes that can occur. Answered by Penny Nom. 





Combinations of 1,2,3,4,5 and 6 
20030201 

From Kyle: Today I was aked a question by my geometry teacher. It was, what is the sum of all the possible combinations of the numbers 1, 2, 3, 4, 5, and 6. He said all the possible combinations were 720. I would like to know how u could do this, and what the answer is. Answered by Penny Nom. 





A penny, a nickel, a dime, a quarter, and a loonie 
20030121 

From Blaine: I have 5 coins: a penny, a nickel, a dime, a quarter, and a loonie. How many different amounts of money could I pay using any combination of these coins? Answered by Penny Nom. 





ALL of the possible 3 digit combinations of 0  9 
20021209 

From Melissa: I need to find out ALL of the possible 3 digit combinations of 0  9. Eg: 000,001,002,003. This is going to take me VERY LONG time. Any suggestions. Answered by Penny Nom. 





Combinations of 1,2,3,...,10 
20021127 

From Gord: If I had the numbers from 110 how many different combinations would i have.....would it be 100....since that is 10 squared. Answered by Penny Nom. 





Social security numbers 
20020906 

From Chris: How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 09 in multiple different spots. Answered by Penny Nom. 





Musical Scales 
20020724 

From Terence: Given that there are 12 notes in a musical octave, what is the maximum number of musical scales possible within that octave, if each scale has a minimum of 5 notes and a maximum of 9 and we start all the scales from the same note? In case you don't know anything about music, a scale is a progression of notes where you start on a specific note and end on that same note an octave higher. There are twelve different notes between these two similar notes. Which notes you choose to play determine the sound of the scale. Anything less than five notes would not make for a very interesting scale. Anything more than nine and you would be playing almost 'every' note in the scale, not leaving much room for distinction in how you organize these notes. I assume you first have to figure out the maximum number of variations possible in a 5note scale (with 12 notes at your disposal). Then do the same for a 6note scale, then a 7note, then an 8note, and so on. Then add up the results. How to find this maximum number of variations for each scale size though is what I don't know. Answered by Leeanne Boehm. 





A popular television game show 
20020519 

From Amrita: On a popular television game show, contestant must first answer a question by placing 4 given events in ascending or desending order in the quickest time. (a) if a contestant does not know how any of the events should be arranged, how many different ways could the question be answered?
Answer: 4!= 24 (b)a contestant has to arrange the events that correspond to A, B, C, and D. one contestant is positive that event D follows directly after avent B, but does not know about the other s. how many different ways could this contestant arrange the letters A, B, C, and D, list the possibility
Answer: which I didn't get Answered by Penny Nom. 





Thank you gifts 
20020515 

From Navi: Children usually attend birthday parties where a thank you gift is given to the children who attent the party. a family likes to hand out books at thankyou gifts. (a) One child invited to the party is given 2 books as gift. if there was 15 different books to choose from, how many diffrent gifts were possible? Answeer: I did this way 15C2=105
(b) if the 15 books consisted of 8 nonfiction and 7 fiction, how many diffrent gifts were possible if at least 1 of 2 books were fiction? Answered by Penny Nom. 





A ski trip 
20020510 

From Navi: A ski trip at the school has been arranged. there are 30 students that have paid for the trip and 6 parents that have volunteered to chaperone. to transport the students and parents easily, they are to be divided into two group. one group has 10 students and 2 parents, and the other group has 20 students and 4 parents. (a) How many different group of 10 students can be formed? ANSWER:
(b) How many different groups consistinmg of 10 students and 2 parents are possible? ANSWER:
(c) kelly is one of the students going on the ski trip, and kelly's mother volunteered to be one of the chaperones. kelly's mother would prefer to be in the smaller group and not in the same group as kelly. if this wish is honoured, how many ways can the smaller group and its chaperones be chosen? ANSWER: Answered by Harley Weston. 





Forming a committee 
20020506 

From Navi: A committee is to be formed to investigate what activites teenagers have available in small communities. the committee is to have 7 members, chosen randomly form interested community members. there are 10 parents, 5 teenagers, and 4 adult without children who have all expressed an interest in serving on the committee. what is the probability that the adults without children are all on the committee? Answered by Andrei Volodin and Penny Nom. 





How many different account numbers are possible? 
20020418 

From Andrene: how many different account numbers are possible if the account numbers consist of a letter of the alphabet, followed by five numerical digits, and followed by another letter. Answered by Penny Nom. 





Combinations? 
20020316 

From Sara: A combination lock has three dials numbered 0  9. Give a mathematical reason why "combination" is a bad name for this type of lock. Answered by Penny Nom and Chris Fisher. 





Permutations and combinations 
20011203 

From Linda: There are 12 people who can be chosen for a project. Q1. Suppose that 2 people refuse to work together. How many groups of 7 can be chosen to work on a project? Q2. Suppose that 2 people insist on working together or neither will work on the project. How many groups of 7 can be chosen to work on the project? Answered by Penny Nom. 





4 digit combinations 
20010922 

From Laura: I need all of the 4 digit combinations using the numbers 09. Answered by Harley Weston. 





Your DJ Business 
20010530 

From Linda: Your DJ Business has 6 rap, 10 rock, 6 alternative, 8 oldies, and 5 country CD singles. How many different 10song sets can the DJ play, if she plays 2 singles from each category? and How many different 10song sets if she plays exactly 3 rap singles and 4 rock singles in each set? Answered by Leeanne Boehm. 





A 6 character field 
20010516 

From A parent: I have a 6 character field that can use any combination of alphanumeric characters (AZ, 09). How many total combinations are possible? Answered by Penny Nom. 





Choosing a car 
20010428 

From Ashley: THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE? Answered by Penny Nom and Andrei Volodin. 





How many 6 digit numeral combinations 
20010426 

From Bryan: How many 6 digit numeral combinations are there If you can only use 6 digits (1, 2, 3, 4, 5, 6) and no number can be used twice in the Numeral! Answered by Claude Tardif. 





A combination lock 
20010405 

From Ken: What is total number of combinations possible on a combination lock which contains 3 wheels each numbered 09? Answered by Penny Nom. 





Lotto 649 
20010227 

From A student: I am a secondary student and I was wondering if there was a better way to find out how many combinations and what they are in the lotto 6/49 than writing them out on a piece of paper. Any help you can provide me with would be greatly appreciated. Answered by Penny Mon. 





Permutations vs. combinations 
20001120 

From Ashleigh: How do you tell whether the problem is a permutation or a combination? Answered by Walter Whiteley. 





Permutations and Multiplication Principle 
20000922 

From Candice: A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side? Answered by Denis Hanson and Claude Tardif. 





4digit numbers using 7, 8, 9 and 0 
20000913 

From Ryan: Could you please help me with the following problem, How many different 4digit numbers are there that use each of the digits 7,8,9,and 0? Please list them. Answered by Penny Nom. 





Cascade 
20000622 

From Peter Bengtsson: Can you help me find an equation for this correlation? 2*1+1 3*2+0 4*2+2 5*3+0 6*3+3 7*4+0 8*4+4 9*5+0 10*5+5 This is the way scores are calculated when you play the game Cascade. The more number of balls you manage to "click away", the better score you get. So, I wrote down lots of results for different amount of balls I clicked away. Clicking away one pair (two adjacent) of balls means 3 points. Clicking away three adjacent balls means 6 points. etc. You can see this from the list above. What I now want to do is to find an equation with only ONE unknown! Y= kn*X+c or something. Whereby I only know X, I can find Y. Answered by Penny Nom. 





Odds and combinations 
20000510 

From Lucy: If the odds are 1/15 of winning, what is the probability? if c 5! 3! How does it equal 10? Answered by Harley Weston. 





Question regarding Combinations and permutations 
20000419 

From Paul Stoner: I am a programmer and I have a quick question. I have 5 criteria which will either be true or false. If a criterion is true it returns its ordinal representation, if false it returns 0. I then combine these results to determine where to go in my program. My question is: How can I figure out the number of combinations I will need? Answered by Patrick Maidorn. 





Ten stools 
20000206 

From Haim: In a cafe with ten stools, three customers want to be seated, so that no two are next to each other. How many ways can this be done? Do not consider it to be a separate seating if two customers switch seats. Answered by Denis Hanson and Walter Whiteley. 





Scheduling Meetings 
19990625 

From Beth Carver: We have 6 groups meeting at three different places simultaneously. The meetings take place once a month each year. Is there a way to have each group meet with each of the other groups at least twice in a year, four times in each place? Answered by Chris Fisher and Harley Weston. 





Triminoes 
19980909 

From Roxanne Hale: I am doing an investigation about a game called triminoes (like dominoes). The game is played using triangular pieces of card. Each card has 3 numbers on it. I have to investigate the relationship between the number of trimino cards in a set and the largest number on the cards. I found; largest no. used 0 1 2 3 4 no. of trimino cards 1 4 10 20 35 I was ginen the formula for this which is: UN= UN  1 + 1/2 (n + 1 ) (n+2) UN=no. of trimino cards n= largest no. I don't know how to get to this equation I think it has something to do with triangle numbers! Answered by Penny Nom. 





Golf problem 
19980825 

From Bob: Twelve golfers plan to play seven rounds of golf. Each would like to play as many rounds with different golfers as possible. What are the optimum combinations to accomplish that goal? Answered by Denis Hanson. 





Divisibility of 2n choose n. 
19960924 

From Kathy Doan: Can you prove that "2n choose n" is not divisible by 3, 5, and 7 for infinitely many n? Answered by Penny Nom. 





How many possible combinations of answers are there? 
19960920 

From David Bester: Suppose there is a 12 question test. Each question can be answered only by true or false. Assuming that all questions are answered (i.e. none are left blank), how many possible combinations of answers are there? And what formula was used to arrive at the answer? Answered by Denis Hanson. 

