Given: P(15, r – 1) : P(16, r – 2) = 3 : 4

To find: value of r

We know,

So, according to question:

P(15, r – 1) : P(16, r – 2) = 3 : 4

⇒ (18 – r) (17 – r) = 12

⇒ 306 – 18r – 17r + r² = 12

⇒ 306 – 12 – 35r + r² = 0

⇒ r² – 35r + 294 = 0

⇒ r² – 21r – 14r + 294 = 0

⇒ r(r – 21) – 14(r – 21) = 0

⇒ (r – 14) (r – 21) = 0

⇒ r = 14 or 21

For, P(n, r): r ≤ n

∴ r = 14 {for, P(15, r – 1)}