A 54-card deck has two jokers in addition to the standard 52 cards (13 face values,...

A 54-card deck has two jokers in addition to the standard 52 cards (13 face values, 4 suits). A joker can be used as any card. For example, the hand with one king, three queens, and a joker can count as a full house, because we can choose the joker to act as a second king.

What is the probability that a random 5-card hand can count as full house? That is: the hand either is a traditional full house (as in class), or the hand contains one or two jokers, which can be chosen in such a way that the hand constituted a full house.

Note: the hand with two kings, two queens, and a joker is only one hand that can count as a full house, even though you can make two different full houses, depending on your choice for the joker.

Explain your final answer. You may leave your final answer as an expression involving binomial coeffi- cients, rather than evaluating them with a calculator.

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orchestra answered 1 year ago

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