Question

Find n if ⁿC_n–2 = 15

Answer 1

ⁿC_n–2 = 15

∴ ⁿC₂ = 15    ...[∵ ⁿC_r = ⁿC_n–r]

∴ `("n"!)/(("n" - 2)!2!)` = 15

∴ `("n"("n" - 1)("n" - 2)!)/(("n" - 2)!2 xx 1)` = 15

∴ n(n – 1) = 30

∴ n(n – 1) = 6 × 5

Equating both sides, we get

∴ n = 6