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Working with permutations. If I...

Working with permutations. If I have 3 items and I choose 13 times that gives me 105 permutations where order is not important or 1, 594, 323 permutations where order is important. I want to expand the 105 groupings one at a time to show how many permutations there would be in them if they were ordered. So for example one of the non-ordered permutation groups has the following items: aaaaaaaaaaaab. If I take that group and make order important instead of one permutation it becomes 13 permutations: aaaaaaaaaaaab, aaaaaaaaaaaba, aaaaaaaaaabaa, etc. That's easy to do by hand but how could I take a group like: aaaaabbcccccc and find all the possible ways to permute it where order is important and the number of each item stays constant? ie. how many ways could a group of 13 items be permuted containing 5 a's, 2 b's and 6 c's?

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