Question

You deal 5 cards from a well-shuffled full deck. (note that there are 52 cards in a full deck and among these, there are exactly 4 aces and 4 kings (likewise 4 of each of the 13 ranks) in the full deck) a) What is the probability that you get exactly 3 aces among the 5 cards? b) What is the probability that you get exactly 2 kings among the 5 cards? c) What is the probability that you get exactly 3 aces and 2 kings among the 5 cards? (note that this counts as a “full house” in poker and is a VERY nice hand to obtain!) d) Why is your answer to part c) not just the product of the answer to part a) times the answer to part b) ? e) A general “full house” in poker is 3 of one rank and 2 in another (eg, 3 aces and 2 fives, or 3 eights and 2 threes, etc…) What is the probability of dealing a full house among the 5 cards?

Answer #1

A standard deck of cards contains 4 suits (Hearts, Diamonds,
Spades, and Clubs) each containing 13 ranks (Ace, 2, 3, 4, 5, 6, 7,
8, 9, 10, Jack, Queen, King) for a total of 52 cards.
In a typical game of poker, you are dealt five cards (without
replacement) from a deck of 52 cards. How many Full Houses are
possible?
(A full house is a hand consisting of three of one rank and two
of another. For instance, three...

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Q19. Consider an ordinary 52-card North American playing deck (4
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