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