Question

If P(11,r) =P(12,r- 1), find r.​

Answer 1

Answer:

Given as P (11, r) = P (12, r – 1) On using the formula, P (n, r) = n!/(n – r)! P (11, r) = 11!/(11 – r)! P (12, r-1) = 12!/(12 – (r-1))! = 12!/(12 – r + 1)! = 12!/(13 – r)! Therefore, from the question, P (11, r) = P (12, r – 1) On substituting the obtained values in above expression we get, 11!/(11 – r)! = 12!/(13 – r)! Now, upon evaluating, (13 – r)! / (11 – r)! = 12!/11! [(13 – r) (13 – r – 1) (13 – r – 2)!] / (11 – r)! = (12×11!)/11! [(13 – r) (12 – r) (11 -r)!] / (11 – r)! = 12 (13 – r) (12 – r) = 12 156 – 12r – 13r + r2 = 12 156 – 12 – 25r + r2 = 0 r2 – 25r + 144 = 0 r2 – 16r – 9r + 144 = 0 r(r – 16) – 9(r – 16) = 0 (r – 9) (r – 16) = 0 r = 9 or 16 For, P (n, r): r ≤ n ∴ r = 9

hope it helps you

. thank you ☺✌