solve for n where it is

Question

p(n,5)=42xP(n-3)

Answer 1

you have a typo
P(n-3) makes no sense.
Did you mean P(n,3) ?

if so, then

n!/(n-5)! = 42n!/(n-3)!
n(n-1)(n-2)(n-3)(n-4) = 42n(n-1)(n-2)
divide by n(n-1)(n-2)
(n-3)(n-4) = 42
n^2 - 7n -30 = 0
(n-10)(n+3)= 0
n=10 or n=-3, but (-3)! is not defined, so

n=10