Let points $A(x,y)$ and $B(x + 1,y)$ be points in an $(m + 1)*(n + 1)$ lattice starting at $O(0,0)$ and ending at $P(m,n)$.

Question

So here is the Question :-

Let points $A(x,y)$ and $B(x + 1,y)$ be points in an $(m + 1)*(n + 1)$ lattice starting at $O(0,0)$ and ending at $P(m,n)$. Show that the number of shortest paths from $O$ to $P$ passing through $AB$ is ${x + y}\choose{x}$${(m - x - 1)+(n - y)}\choose{m - x - 1}$ .

While reading the problem I understood the meaning of it . But I absolutely have no idea of how to prove the fact that it is always ${x + y}\choose{x}$${(m - x - 1)+(n - y)}\choose{m - x - 1}$ . Can anyone help me do it?

Any hints and suggestions for this problem will be greatly appreciated .