Question

Find n if ⁿC_n–3 = 84

Answer 1

ⁿC_n–3 = 84

∴ `("n"!)/(("n" - 3)!["n" - ("n" - 3)]!)` = 84

∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)! xx 3!)` = 84

∴ n(n – 1)(n – 2) = 84 × 6

∴ n(n – 1)(n – 2) = 9 × 8 × 7

Comparing on both sides, we get n = 9