Quandaries
and Queries 

My level of question is secondary. 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... Thank you for your time and effort. Tom 

Hi Tom, In your first problem the examples you list don't have any digits repeated so I am going to assume that you are looking for 4 digit strings made from the digits from 1 to 7 with no digit repeated. Think about constructing such a string. You start by writing one digit. You have 7 choices of digit. Now you write down a second digit. This time you only have 6 choices since you can't repeat the first digit. That is each one digit number you can extend to a two digit number in 6 ways.
Now add a third digit, you have 5 choices. That is each two digit number you can extend to a three digit number in 5 ways.
Likewise for the fourth digit.
For your second problem I am going to assume that the two special digits are known before you start, so in your example you know that 1 and 2 must be included. Place the two special digits first. You have 4 choices for the position of the first special digit and then 3 choices for the position of the second.
Now you have two more positions to fill from the five remaining "nonspecial" digits. Chose one of them and put it in the first vacant position. You have 5 choices as to which digit you chose. Now chose one of the four remaining to go into the one remaining position. There are 4 choices.
Penny 

