What is the probability that a hand has exactly two hearts given that it has the 2 of hearts? . A card game is played with a deck whose cards can be one of 6 suits, one of the suits being hearts, and one of 11 ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts given that it has the 2 of hearts? Please explain.

There are $\binom{65}{2}$ hands with the two of hearts, all equally likely. (I'm assuming the deck has 66 cards - one for every suit/rank pair.)
Of those, how many hands have the two of hearts, another heart, and a non-heart?
