Cardinality of the intersection of two random sets

Assuming $M\le N$, $$ P(|X_k\cap Y_j|=c)=\frac{\binom Mc\binom{M-c}{j-c}\binom{N-j}{k-c}}{\binom M j\binom N k}, $$ as there are $\binom M c$ ways of choosing the intersection, $\binom{M-c}{j-c}$ ways of choosing the rest of the elements of $Y_j$, and $\binom{N-j}{k-c}$ ways of choosing the rest of the elements of $X_k$.