Joint probability function (3 Cards without replacement)

Question

I have the following problem:

3 Cards are picked from a deck without replacement. Let $X$ number of hearts and $Y$ number of diamonds. Find the joint probability function.

I know $X$ and $Y$ are both discrete random variables that can take on 0, 1, 2 and 3. Therefore:

$$\mathbb{P}\left(X=i,Y=j\right)=??\qquad\forall i,j\in\left\{ 0,1,2,3\right\} $$

Answer 1

It is a multivariiate hypergemoteric distribution.

You seek the probability for selecting $i$ from $13$ hearts, $j$ from $13$ diamonds, and $3-i-j$ from $26$ other suits when selecting $3$ from $52$ cards.