Solve the equation nP5/nC3=12

Answer 1

n!/(n-5)! / n!/(3!(n-3)!) = 12
6(n-3)!/(n-5)! = 12
(n-3)! = 2(n-5)!
(n-3)(n-4)(n-5)~ = 2(n-5)!
(n-3)(n-4) = 3*1
n-3 = 2
n = 5

check: 5P5 = 120
5C3 = 10
120/10 = 12