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Problem: Determine the number of permutations of the characters for: AABBBC

How can I calculate a problem like this generally, given a set of characters and a number of times each has to appear?

golom889
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  • For a different approach, there are $\binom{6}{1}$ ways to choose where the C will go,and for each such choice there are $\binom{5}{2}$ ways to choose where the two A's will go, for a total of $\binom{6}{1}\binom{5}{2}$. – André Nicolas May 06 '15 at 03:57

1 Answers1

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Presumably you know six distinct letters can be rearranged in $6!$ distinct ways.   A straightforward count of permutations.

Now suppose two of those letters were not distinct.   $\rm BEA_1A_2CD$ is indistinguishable from $\rm BEA_2A_1CD$ when the numbers rub off, and so forth.   Every arrangement is one of a set of arrangement where only the identical letters are in different positions.   There are $2!$ ways to arrange two distinct letters, so what we need to do is divide by that.

There are $6!/2!$ distinct ways to rearrange $\rm AABCDE$.

Can you now count the distinct ways to rarrange $\rm AABBBC$?

Graham Kemp
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