Start out by replacing the value of Y by N-X.
You then get
P(N-X) = (N N-X) * [P^(N-X)] * [(1-P)^(N-(N-X))]
P(N-X) = (N N-X) * [(1-P)^X] * [P^(N-X)
Then just expand the combination and prove that it is equal to (N X).
The last step is to define a new variable P' = 1-P, which is the probability parameter for Y.
