If 15Cr : 15Cr – 1 = 11 : 5, find r.

Q9 of 118 Page 18

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

Given:

⇒

We know that

And also n! = n(n – 1)(n – 2)…………2.1

⇒

⇒ 5(16 – r) = 11r

⇒ 80 – 5r = 11r

⇒ 16r = 80

⇒

⇒ r = 5

∴ The value of r is 5.

If ¹⁵C_3r = ¹⁵C_{r + 3}, find r.

If ⁸C_r – ⁷C₃ = ⁷C₂, find r.

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

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