Permutations. Permutations with repetition

Permutations of $n$ distinct elements

The number of permutations of $n$ pairwise distinct objects is $P_n=n!=1\cdot2\cdot\ldots\cdot n.$ All objects participate; order on the slots matters. Permutations with repetition: if type $i$ appears $n_i$ times, $\sum n_i=n$ , then $P=\dfrac{n!}{n_1!\,n_2!\,\ldots\,n_r!}.$

$0!=1$ — a convention stable in formulas

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