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There are n! ways to rearrange n objects. If there are N objects in total, of which n1 identical objects of type 1, n2 of type 2,... nk of type k...etc., such that the different type of objects are distinguishable, then we can compute the number of distinguishable permutations as follows. Suppose the number of distinguishable permutations is p. Then suppose that the identical objects turn ...
From the fact that there are N! ways to permute N distinct numbers, we explain how to compute the number of distinguishable permutations of letters in a word.