More generally, for an -element multiset having distinct elements with copies of the distinct element (so ), the number of permutations equals the multinomial coefficient, given by Multinomial.There are therefore permutations of, namely, ,, , and. There are permutations of a list of (distinct) elements, a fact that follows from there being spots to place the first element, spots to place the second element once the first is placed, spots to place the third element once the first two elements are placed and so on until a single spot remains in which to place the last element. Factorials are best known for counting fixed orderings of the elements of a list, known as permutations, which can be generated using Permutations.Factorials of half integers are given by rational multiples of. For a general complex number, , where the Gamma function is defined by for all complex values of except when is a negative integer (in which case is complex infinity). The special case is defined as 1, consistent with the combinatorial interpretation of there being exactly one way to arrange zero objects. In particular, Factorial returns the factorial of a given number, which, for positive integers, is defined as.

Factorial represents the factorial function.

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