Find in how many ways we can arrange the letters AABBBC taken three letters at a time
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Answers
How many times I can arrange letters: A A B B C C ?
I need to solve two problems and one I already solved.
First: first A and second A are the same letters (repeated items in permutations). So I just have
6!2!⋅2!⋅2!
2! is for each letter. It reduces permutations from 720 to 90. That's good.
Second unsolved: I want to also exclude circular sequences. By circular I mean A A B B C C is the same as A B B C C A (also B B C C A A, B C C A A B and so on...) - imagine those letters are around circle, we just changed letter that we started to read from, but it is still same sequence.
I will attach pictures later if description is not sufficient.
The truth is I don't really need a count but a list of all those sequences - but it can be ignored, for now I want to solve second problem. It should be around 16 of them. I could just write it by hand (I have ready list) but I wanted to use an algorithm - I do it just for fun and to learn something new.