Permutation

A permutation of a set is an arrangement of its elements in a definite order. The number of permutations of $n$ distinct objects is $n!$ (n factorial).

Permutations can also be viewed as bijective functions from a set to itself. Under composition, the permutations of a set form a group — the symmetric group $S_n$. This is one of the most important examples of a non-abelian group (for $n \geq 3$).

A $k$-permutation of $n$ objects is an ordered selection of $k$ objects from $n$, numbering $\frac{n!}{(n-k)!}$.