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 a 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 ${}^n P_r = n^{\underline r}$