Vtyjkyuk

I've been working though a problem which deals with the following:
In a card game there are four players $p_1,p_2,p_3,p_4$ each of these players is uniformly at random dealt 13 cards. What would be the probability that $p_1$ and $p_2$ are dealt all the hearts in the deck?

I've been thinking it would be something like:
$$frac39 choose 13cdot26 choose 13cdot1 52 choose 13 39 choose 13 26 choose 13.$$ But I'm not convinced this is the right answer. Can someone put me on the right track here?

Thanks!

Having one pair get all the hearts means that the other pair has gotten all the non-hearts cards. There's 39 of those, and the other pair has to get 26 of them. This is compared to the space of picking 26 cards from the whole deck of 52.

$$fracbinom3926binom5226=frac191160054approx1.164times10^-5$$

Total ways of distributing 52 cards in 4 players are
$$ binom5213binom3913binom2613 $$

Number of ways distributing hearts in two players $p_1$ and $p_2$ is

First, take 13 hearts out of the deck now you have 39 cards in hand take 13 cards out of these 39 to distribute in $p_1$ and $p_2$ now you have 26 cards to distribute in $p_1$ and $p_2$ and distribute the remaining 26 cards in $p_3$ and $p_4$

$$Ways=binom3913cdotbinom2613binom2613$$

Probability is $$fracbinom3913binom2613binom2613 binom5213binom3913binom2613=fracbinom2613binom5213$$