In Binomial distribution, the number of trials follows the Binomial distribution

Question

We consider the following two random variables: $X \sim Binomial(1+N,\alpha)$ and $N \sim Binomial (W,\delta)$

Then does the following hold? $P(X=x,N=y)=$${1+y}\choose{x}$ $\alpha^x(1-\alpha)^{1+y-x}$