Permutation without Repetition

combinatorics

Definition

Permutation without Repetition

A permutation without repetition is an ordered rearrangement of distinct elements.

All possible rearrangements of a $n$-tuple can be counted using:

$$n!=n(n-1)(n-2)\dots 3\cdot 2\cdot 1$$

by the product rule.

Example: The tuple $(1,2,3)$ can be rearranged as:

$$(1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1)$$