# Combinations from a repeting set

• Dec 9th 2011, 02:49 AM
dipsy34
Combinations from a repeting set
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 $10!/2*2*2$? since we always get 3 letters that goes in twice the combination.
• Dec 9th 2011, 03:09 AM
Plato
Re: Combinations from a repeting set
Quote:

Originally Posted by dipsy34
How many 10 long combinations can you make from the repeating set A = {a,b,c,d,e,f,g}

This is too vague to know what is to be counted. If we select ten from that set at least one letter is repeated up to four times.

Please tell us more about how the strings are composed.
• Dec 12th 2011, 04:15 PM
HallsofIvy
Re: Combinations from a repeting set
What do you mean by "repeating" set? You say "the repeating set {a, b, c, d, e, f, g}" but there are no "repetitions" in that. Do you mean, for example, that "a" and "b" might represent the same object?
• Dec 17th 2011, 06:58 AM
vincisonfire
Re: Combinations from a repeting set
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.