Question

A 5-card hand is dealt from a deck of 52 cards. what is the probability that 4 are hearts

Answer 1

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You're essentially dealing a three-card hand from a deck of 50 (missing the spade and heart kings), wanting to know the probability of getting the remaining two kings among those three. The number of ways of dealing three cards is 50C3=1960050C3=19600; the number of hands with two kings is 4848 (one for each of the remaining cards in the hand); so the probability is 48/19600=3/122548/19600=3/1225.