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

Q10 of 118 Page 18

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.

If ⁸C_r – ⁷C₃ = ⁷C₂, find r.

If ¹⁵C_r : ¹⁵C_{r – 1} = 11 : 5, find r.

If ²⁸C_2r : ²⁴C_{2r – 4} : 225 : 11, find r.

If ⁿC₄, ⁿC_5, and ⁿC₆ are in A.P., then find n.