Definition:Permutation/Ordered Selection

Definition
Let $S$ be a set of $n$ elements.

Let $r \in \N: r \le n$.

An $r$-permutation of $S$ is an ordered selection of $r$ elements of $S$.

From this definition, it can be seen that a bijection $f: S \to S$ (defined as a mapping) is an $n$-permutation.

Also known as
A permutation as used in this context is also known as an arrangement or rearrangement.

The term ordered selection is also used when it is necessary to distinguish this concept precisely from that of a bijection from a set to itself.

Also see

 * Definition:Permutation on n Letters


 * Number of Permutations, where it is shown that:
 * ${}^n P_r = \dfrac {n!} {\paren {n - r}!}$
 * ${}^n P_n = n!$


 * Definition:Falling Factorial, where it can be seen that ${}^n P_r = n^{\underline r}$