Question -
Answer -
Given:
P (n, 4) = 12. P (n,2)
By using the formula,
P (n, r) = n!/(n – r)!
P (n, 4) = n!/(n – 4)!
P (n, 2) = n!/(n – 2)!
So, from the question,
P (n, 4) = 12. P (n,2)
Substituting theobtained values in above expression we get,
n!/(n – 4)! = 12 ×n!/(n – 2)!
Upon evaluating,
n! (n – 2)! / n! (n –4)! = 12
[(n –2) (n – 2 -1) (n – 2 – 2)!] / (n – 4)! = 12
[(n –2) (n – 3) (n – 4)!] / (n – 4)! = 12
(n – 2) (n – 3) = 12
n2 –3n – 2n + 6 = 12
n2 –5n + 6 – 12 = 0
n2 –5n – 6 = 0
n2 –6n + n – 6 = 0
n (n – 6) – 1(n – 6) =0
(n – 6) (n – 1) = 0
n = 6 or 1
For, P (n, r): n ≥ r
∴ n =6 [for, P (n, 4)]