Permutation of n objects with repetitions

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If there are n objects with $$n_1$$ identical of type 1, $$n_2$$ identical of type 2, ..., $$n_k$$ identical of type k ($$n_1 + n_2 + \dots + n_k = n$$), then the number of distinct permutations is:

$$ \frac{n!}{n_1! n_2! \dots n_k!} $$
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