Question

Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3

Answer 1

`("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3

∴ `("n"!)/(3!("n" - 5)!)xx(5!("n" - 7)!)/("n"!) = 10/3`

`∴("n"!)/(3!("n"-5)("n"-6)("n"-7)!)xx(5xx4xx3!("n"-7)!)/("n"!)=10/3`
∴ `(5xx4)/(("n" - 5)("n" - 6)) = 10/3`
∴ (n – 5) (n – 6) = 3 × 2
Comparing on both sides, we get
∴ n – 5 = 3
∴ n = 8