A poker hand consists of five cards drawn from a deck of 52 cards.  Each card has one of 13 denominations (2,3,4,...10,Jack,Queen,Ace) and one of four suits (spades, hearts, diamonds, clubs).Determine the probability of drawing a "full house" (three cards of one denomination and two cards of another denomination)

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Asked Mar 6, 2019
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A poker hand consists of five cards drawn from a deck of 52 cards.  Each card has one of 13 denominations (2,3,4,...10,Jack,Queen,Ace) and one of four suits (spades, hearts, diamonds, clubs).

Determine the probability of drawing a "full house" (three cards of one denomination and two cards of another denomination)

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Expert Answer

Step 1

Event A denotes that among the five cards drawn, three cards of one denomination and two card of another denomination.

The probability of the event A is obtained as shown below:

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Step 2

Here, there are 52 cards and each card has one of the 13 denominations. In 13C3 ways one can draw three cards of one denomination and from the remaining 10 cards two cards are selected in10C2 ways. The five cards can be selected in 52C5...

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