If ^{n + 2}C₈ : ^{n – 2}P₄ = 57 : 16, find n.

Given:

⇒

We know that ,

And also n! = n(n – 1)(n – 2)…………2.1

⇒

⇒

⇒

⇒

⇒ (n + 2)(n + 1)(n)(n – 1) = 21 × 20 × 19 × 18

Equating the corresponding terms on both sides we get,

⇒ n = 19

∴ The value of n is 19.