if X and Y are discrete RVs with pmf $\displaystyle p(x,y) = a\; \dfrac{k!}{x!y!(k-x-y)!}$ where x and y are$\displaystyle non \; negative \; integers \; and\; x+y\leq k$.

I want to find the value of a.

I know that I need to show that the pmf sums up to 1.

$\displaystyle \sum_x \sum_y p(x,y)=1$

since x and y are non negatve: 0<=x+y<=k

here i am getting confused in where x and y range from.

can anyone help me how to solve this?