permutation

An arrangement of items where order matters — counted by P(n,r).

A permutation is an arrangement of items in which order matters, so swapping two chosen items produces a genuinely different outcome. The number of permutations of $r$ items chosen from $n$ distinct items is $P(n,r)=\dfrac{n!}{(n-r)!}$ , equal to $n$ counting-principle blanks multiplied together starting at $n$ and counting down $r$ places.

Examples

Awarding gold, silver, and bronze among 7 racers is a permutation: $P(7,3)=7\times6\times5=210$ .