Question

Find n if `""^"n""C"_("n" - 3)` = 84

Answer 1

`""^"n""C"_("n" - 3)` = 84

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

∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)!xx3!` = 84

∴ n (n – 1) (n – 2) = 84 × 6

∴ n (n – 1) (n – 2) = 9 × 8 × 7
Comparing on both sides, we get n = 9