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 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. Thanks,

The page Robert sent us is generated by the lottery page on WebMath. On their page input 5 in response to "How many correct numbers must you choose in order to win?", 1 for "What is the lowest number you can choose?" and 39 for "What is the highest number you can choose?" and then select What are my odds?

Robert,

Just to be clear, there are (39 choose 5) = 575, 757 different lottery tickets. The number 120 just comes up in calculating this value. It represents the number of different orders that a person could mark off the five boxes on his ticket.

For example, suppose you wanted to buy a ticket with the numbers 1, 2, 3, 4, 5. When you fill out the ticket, you could mark the boxes box with 1 first, then 2, then 3 and so on. Or you could mark the boxes in a different order. Maybe you mark off the box with 3 first, then 5, etc. There are 120 different ways. It doesn't matter what the five numbers are. There are 120 orders in which 5 numbers can be listed (there are 120 permutations of 5 distinct objects).

I was able to get the list below by using the Combinatorial Object Server at http://theory.cs.uvic.ca/cos.html
and asking for permutations of 1, 2, 3, 4, 5. Just put in 5 for n and leave the other boxes blank.

Hope this helps.
Victoria

5, 4, 3, 2, 1
5, 4, 3, 1, 2
5, 4, 1, 3, 2
5, 1, 4, 3, 2
1, 5, 4, 3, 2
5, 4, 2, 3, 1
5, 4, 2, 1, 3
5, 4, 1, 2, 3
5, 1, 4, 2, 3
1, 5, 4, 2, 3
5, 2, 4, 3, 1
5, 2, 4, 1, 3
5, 2, 1, 4, 3
5, 1, 2, 4, 3
1, 5, 2, 4, 3
2, 5, 4, 3, 1
2, 5, 4, 1, 3
2, 5, 1, 4, 3
2, 1, 5, 4, 3
1, 2, 5, 4, 3
5, 3, 4, 2, 1
5, 3, 4, 1, 2
5, 3, 1, 4, 2
5, 1, 3, 4, 2
1, 5, 3, 4, 2
5, 3, 2, 4, 1
5, 3, 2, 1, 4
5, 3, 1, 2, 4
5, 1, 3, 2, 4
1, 5, 3, 2, 4
5, 2, 3, 4, 1
5, 2, 3, 1, 4
5, 2, 1, 3, 4
5, 1, 2, 3, 4
1, 5, 2, 3, 4
2, 5, 3, 4, 1
2, 5, 3, 1, 4
2, 5, 1, 3, 4
2, 1, 5, 3, 4
1, 2, 5, 3, 4
3, 5, 4, 2, 1
3, 5, 4, 1, 2
3, 5, 1, 4, 2
3, 1, 5, 4, 2
1, 3, 5, 4, 2
3, 5, 2, 4, 1
3, 5, 2, 1, 4
3, 5, 1, 2, 4
3, 1, 5, 2, 4
1, 3, 5, 2, 4
3, 2, 5, 4, 1
3, 2, 5, 1, 4
3, 2, 1, 5, 4
3, 1, 2, 5, 4
1, 3, 2, 5, 4
2, 3, 5, 4, 1
2, 3, 5, 1, 4
2, 3, 1, 5, 4
2, 1, 3, 5, 4
1, 2, 3, 5, 4
4, 5, 3, 2, 1
4, 5, 3, 1, 2
4, 5, 1, 3, 2
4, 1, 5, 3, 2
1, 4, 5, 3, 2
4, 5, 2, 3, 1
4, 5, 2, 1, 3
4, 5, 1, 2, 3
4, 1, 5, 2, 3
1, 4, 5, 2, 3
4, 2, 5, 3, 1
4, 2, 5, 1, 3
4, 2, 1, 5, 3
4, 1, 2, 5, 3
1, 4, 2, 5, 3
2, 4, 5, 3, 1
2, 4, 5, 1, 3
2, 4, 1, 5, 3
2, 1, 4, 5, 3
1, 2, 4, 5, 3
4, 3, 5, 2, 1
4, 3, 5, 1, 2
4, 3, 1, 5, 2
4, 1, 3, 5, 2
1, 4, 3, 5, 2
4, 3, 2, 5, 1
4, 3, 2, 1, 5
4, 3, 1, 2, 5
4, 1, 3, 2, 5
1, 4, 3, 2, 5
4, 2, 3, 5, 1
4, 2, 3, 1, 5
4, 2, 1, 3, 5
4, 1, 2, 3, 5
1, 4, 2, 3, 5
2, 4, 3, 5, 1
2, 4, 3, 1, 5
2, 4, 1, 3, 5
2, 1, 4, 3, 5
1, 2, 4, 3, 5
3, 4, 5, 2, 1
3, 4, 5, 1, 2
3, 4, 1, 5, 2
3, 1, 4, 5, 2
1, 3, 4, 5, 2
3, 4, 2, 5, 1
3, 4, 2, 1, 5
3, 4, 1, 2, 5
3, 1, 4, 2, 5
1, 3, 4, 2, 5
3, 2, 4, 5, 1
3, 2, 4, 1, 5
3, 2, 1, 4, 5
3, 1, 2, 4, 5
1, 3, 2, 4, 5
2, 3, 4, 5, 1
2, 3, 4, 1, 5
2, 3, 1, 4, 5
2, 1, 3, 4, 5
1, 2, 3, 4, 5

Permutations = 120

Robert wrote back

Hi,

Thanks for your help, I am very sorry to say, I can not find the answer to my question, on non or those sites, once again, how does they come up with the (120) combinations, I have tried everything I can, but I still can not come up with no (120) combinations.

Please help me with the (120) combinations, when you chose 5 numbers, from 39 numbers, when you can not repeat none of your numbers within the (120) combinations.

You gave me a listing of numbers 1 to 5, I am asking you for a listing of number from 1 to 39, when you can only chose 5 of the numbers, without repeating none of your combination.

The web site where I found the question, does not give me no way to contact them for a answer.

Thanks,

Robert

Robert,

You say "I am asking you for a listing of number from 1 to 39, when you can only chose 5 of the numbers". That listing is not a list of length 120 but a list of length 575,757. The number 120 that is in the calculations on the web page you sent to us is the number of choices you have AFTER you have decided what numbers to play in the lottery. In Victoria's example she decided to play the five numbers 1, 2, 3, 4 and 5. She then has to write these 5 numbers on the lottery ticket. She can write the in any order maybe

1, 2, 3, 4, 5

or

5, 4, 3, 2, 1

or

1, 2, 3, 5, 4

or

.....

In fact there are 120 ways she can write her five numbers on the lottery ticket.

Harley

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