P (n, 6) = 5P(n, 5) we have
n! 5 n!
_______ = _______ divide out n!
(n - 6)! (n - 5)!
1 = 5
____ _______ cross-multiply
(n - 6)! (n - 5)!
(n - 5)! = 5(n - 6)! Note that we can write (n - 5)! as (n - 5) (n - 6)!
(n -5) (n - 6)! = 5(n - 6) ! divide both sides by (n - 6)!
n - 5 = 5
n = 10
Proof
P(10, 6) = 151,200
5P(10 - 5) = 151,200