permutation

A permutation of a set is an arrangement of its elements into a sequence, where the order of the elements matter.

For example, the 6 permutations (orderings) of the set {1, 2, 3} are (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).

For a set with $n$ distinct elements, the number of permutations possible if we pick $k$ elements from the set and ordered them is called a k-permutation, represented as $P(n,k)$.

$P(n,k)=\frac{n!}{(n-k)!}$

guide to permutations and combinations