Question

Problem 6 Five cards are dealt from a standard 52-card deck. Note that there are 13 kind of cards and each kind has 4 cards in a standard deck. (a) How many ways that one can draw 3 aces and 2 kings? (0.5 point (b) How many ways that one can draw a full house (3 cards of one kind, 2 cards of another kind)? (0.5 point)

Answer 1

(a)

There are 4 aces and 4 kings so number of ways of selecting 3 aces and 2 kings is

Answer: 24

(b)

Number of ways of selecting 1 denominations out of 13 is C(13,1). Number of ways of selecting 3 cards out of 4 cards of selected denomination is C(4,3). And then select one denomination out of remaining 12 denominations is C(12,1) and then 2 cards from each selected denominations is C(4,2). So number of ways are there to draw a 5 card poker hand that contains 3 a kind and 2 a kind is

C(13,1)C(4,3)C(12,1)C(4,2) = 3744 ways