Card Deck Probability

Question

Five cards are dealt from a regular deck of 52 cards. (Recall that a regular deck of 52 cards consists of 13 kinds/denominations, each having 4 suits: ♥, ♦, ♣ ♠.)

Part a)

What is the probability that you get a full house (i.e. three of one kind and two of another kind) if the first two cards you were dealt were two aces? Do NOT round answer.

Part b)

Now, what is the probability that you get three of a kind (i.e. three cards of one kind plus two other cards, each of different kinds) if the first two cards you were dealt were two aces? Note that a full house does not count as three of a kind. Do NOT round answer.

Answer 1

a)3/51*1/25*1/49*3=120825

b) 1/5*47/49*1/16*47/16 = 2209/62720