# permutation

A permutation of a set of objects is an ordering of those objects. For instance, the possible permutations of the set $$\{a,b,c\}$$ are $$abc$$, $$acb$$, $$bac$$, $$bca$$, $$cab$$, and $$cba$$.

The number of distinct permutations of all the elements of a set of $$n$$ elements is given by $$n!$$ ($$n$$ factorial), i.e. the product

$n \times (n-1) \times (n-2) \times \cdots \times 3 \times 2 \times 1.$

More generally, the number of permutations of a subset of $$r$$ elements chosen from a set of $$n$$ elements is given by the permutations formula

$\displaystyle\frac{n!}{(n-r)!},$

generally denoted by $$_nP_r$$ and described as “$$n$$ permute $$r$$.”