11TH•Mathematics•Permutations And Combinations•7.3 Objects Not All Different

7.3 Permutation of Objects Not All Different

Permutations with repeated objects and circular permutations.

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If among $n$ objects there are $n_1$ alike of one kind, $n_2$ of another, etc., then

\dfrac{n!}{n_1!\, n_2!\, n_3!\, \cdots}

distinct arrangements (taken all at a time).

MISSISSIPPI ( $11$ letters: I×4, S×4, P×2, M×1):

\dfrac{11!}{4!\,4!\,2!\,1!} = 34650

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