# permutations with identical items.

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

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3. 👁 149
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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