Question

nP5 = 120 x nC3

Answer 1

First you have to understand the meaning of the notation. I assume you are solving for n.

nP5 is the number of ways of selecting, in a particular order, 5 distinct objects from a group of n. These are called permutations. The number nP5 equals n(n-1)(n-2)(n-3)(n-4)

nC3 is the number of distinct ways of selecting 3 objects from a group of the same number n, regardless of order. These are called combinations. The number nC3 equals
n(n-1)(n-2)/3!

If
nP5 = 120 nC3, then
n(n-1)(n-2)(n-3)(n-4)
= 120*n(n-1)(n-2)/3! ,
then
(n-3)(n-4) = 20
which requires that
n = 8

Answer 2

nP5/nC3=12