Question -
Answer -
Given:
P (11, r) = P (12, r –1)
By 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)!
So, from the question,
P (11, r) = P (12, r –1)
Substituting theobtained values in above expression we get,
11!/(11 – r)! =12!/(13 – r)!
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 [for, P (11, r)]