Find n if ⁿP₄ = 20 × ⁿP₂.

Step 1. Write out the products. $n(n - 1)(n - 2)(n - 3) = 20\, n(n - 1)$.

Step 2. Cancel. Since $n \ge 4$, divide by $n(n - 1)$: $(n - 2)(n - 3) = 20$.

Step 3. Solve. Two whole numbers in a row multiply to $20$: $5 \times 4$. So $n - 2 = 5$ and $n = 7$.