Question

Find n, if ⁿP₆ : ⁿP₃ = 120 : 1

Answer 1

ⁿP₆ : ⁿP₃ = 120 : 1

∴ `("n"!)/(("n" - 6)!) divide ("n"!)/(("n" - 3)!) = 120/1`

∴ `("n"!)/(("n" - 6)!) xx (("n" - 3)!)/("n"!)` = 120

∴ `("n"!)/(("n" - 6)!) xx (("n" - 3)("n" - 4)("n" - 5)("n" - 6)!)/("n"!)` = 120

∴ (n – 3) (n – 4) (n – 5) = 120

∴ (n – 3) (n – 4) (n – 5) = 6 × 5 × 4

Comparing on both sides, we get

n – 3 = 6

∴ n = 9