Question -
Answer -
Given:
P(n, 5) : P(n, 3) = 2: 1
P(n, 5) / P(n, 3) = 2/ 1
By using the formula,
P (n, r) = n!/(n – r)!
P (n, 5) = n!/ (n –5)!
P (n, 3) = n!/ (n –3)!
So, from the question,
P (n, 5) / P(n, 3) = 2/ 1
Substituting theobtained values in above expression we get,
[n!/(n – 5)!] / [n!/ (n – 3)!] = 2/1
[n!/(n – 5)!] × [(n – 3)! / n!] = 2/1
(n – 3)! / (n – 5)! =2/1
[(n –3) (n – 3 – 1) (n – 3 – 2)!] / (n – 5)! = 2/1
[(n –3) (n – 4) (n – 5)!] / (n – 5)! = 2/1
(n – 3)(n – 4) = 2
n2 –3n – 4n + 12 = 2
n2 –7n + 12 – 2 = 0
n2 –7n + 10 = 0
n2 –5n – 2n + 10 = 0
n (n – 5) – 2(n – 5) =0
(n – 5) (n – 2) = 0
n = 5 or 2
For, P (n, r): n ≥ r
∴ n =5 [for, P (n, 5)]