## Definition A ==Permutation== is an arrangement of $k$ objects selected from $n$ distinct objects where the **order matters**. The number of permutations is: $ P(n, k) = \frac{n!}{(n-k)!} $ > [!example]- In how many ways can a president, vice president, and secretary be chosen from a club of 12 members? > Order matters (different roles), so we use a permutation: > $ P(12, 3) = \frac{12!}{9!} = 12 \times 11 \times 10 = 1{,}320 $