SOLUTION: If 5 cards are drawn at random from a deck of 52, what is the probability of pulling 3 cards of one denomination and 2 cards of a second denomination?

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Question 1120908: If 5 cards are drawn at random from a deck of 52, what is the probability of pulling 3 cards of one denomination and 2 cards of a second denomination?
Answer by greenestamps(13200) About Me  (Show Source):
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(1) # of ways of choosing 2 of the 13 denominations: 13C2 = (13*12)/2 = 78

(2) # of ways of choosing 1 of those 2 denominations to be the one to have 3 of a kind: 2C1 = 2

(3) # of ways of choosing 3 of the 4 cards of the first denomination: 4C3 = 4

(4) # of ways of choosing 2 of the 4 cards of the second denomination: 4C2 = 6

(5) # of ways of choosing 3 cards of one denomination and 2 of another: 78*2*4*6 = 3744

Probability of choosing 3 cards of one denomination and 2 of another: 3744/(52C5) = 3744/2598960 = .00144 (to 5 decimal places)