If 28C2r : 24C2r – 4 : 225 : 11, find r.

Q11 of 118 Page 18

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

Given:

⇒

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

⇒ (2r)(2r – 1)(2r – 2)(2r – 3) = 11 × 12 × 13 × 14

Equating the corresponding terms on both sides we get,

⇒ 2r = 14

⇒

⇒ r = 7

∴ The value of r is 7.

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

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

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

If ²ⁿC₃ : ⁿC₂ = 44 : 3, find n.