How many 10 long combinations can you make from the repeating set A = {a,b,c,d,e,f,g}
I was supposed to express this in factorials.
What confuses me is the fact that its a repeating set and how this affects the solution. I'm guessing that it would mean that 10 long combinations would look something like this: abcdefgabc,bcdefgabcd, cdefgabcde which would mean that the answer would be ? since we always get 3 letters that goes in twice the combination.
I think the way to think about this is the following.
You have 10 objects ++++++++++.
The different combinations can be counted in terms of "cuts" |.
For example:
++|+++|++++|+||| = aabbbccccd;
||++|++++|++|+|+ = ccddddeef.
You must count the number of "cuts" you can make. Note that cuts are indistinguishable.
I think you can get it from there.