# If P(15, r – 1) : P(16, r – 2) = 3 : 4, find r.

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)}

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