permutations with identical items.

how many four letter arrangements are there for the word Mattawa?

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asked by Anon
  1. There are 7 letters, so there are 7! ways to arrange them. But, the two t's and 3 a's are indistinguishable.

    Since there are 2! ways to arrange the 2 t's, we divide by 2! to get the number of unique permutations.

    Similarly for the 3 a's.

    So, the final count is 7!/(2!3!) = 120

    There are still 7! arrangements, but only 1/6 of them can be distinguished.

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    posted by Steve
  2. I sure am glad you came along and was headed the same way you were but note there are only 4 letters arrangements allowed.
    That ended me up with
    7!/ [ 4!*3! *3!*2! ]
    or
    35/12
    and a fractional answer did not make sense to me

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    posted by Damon

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