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 $\displaystyle 10!/2*2*2$? since we always get 3 letters that goes in twice the combination.

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.**

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?

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.