Variation without Repetition

combinatorics

Definition

Variation without Repetition

A variation without repetition are ordered selections of $k$ different elements out of $n$.

All possible variations of a set of length $n$ can be counted using:

$$n(n-1)\dots (n-k+2)(n-k+1)=\frac{n!}{(n-k)!}=k!\left(\genfrac{}{}{0ex}{}{n}{k}\right)$$

by the product rule.