Explanation Given: 2 cards are dealt to each player with additional 5 cards on the table shared by all players from a deck of 52 cards in the card game Texas Hold’Em. Explanation: Consider the experiment of dealing 2 cards to each player and sharing 5 cards on the table by all players from a deck of 52 cards. The number of elements in the sample space will be equal to the number of ways of selecting 2 + 5 = 7 cards from 52 cards. That is, n ( S ) = C ( 52 , 7 ) = 52 ! 7 ! × ( 52 − 7 ) ! = 52 × 51 × 50 × 49 × 48 × 47 × 46 × 45 ! 7 × 6 × 5 × 4 × 3 × 2 × 1 × 45 ! = 133 , 784 , 560 Assume that, E represents the event of getting three of a kind hand. Three of a kind hand contains 3 cards of one value with other cards of four different values. A deck has cards with 13 different values, so, first card has 13 choices. There are four cards in a deck with same value, so, the number of ways of choosing three cards from four cards of same value will be C ( 4 , 3 )

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.3, Problem 61E

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The probability of getting three of a kind in the game of Texas Hold’Em with 2 cards dealt and additional 5 cards on the table shared by all players.

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Chapter 8.3, Problem 60E

Chapter 8.3, Problem 62E

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Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

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The probability of getting three of a kind in the game of Texas Hold’Em with 2 cards dealt and additional 5 cards on the table shared by all players.

Solution Summary: The author analyzes the probability of getting three of a kind in Texas Hold'Em with 2 cards dealt to each player and additional 5 cards on the table shared by all players.

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The probability of getting three of a kind in the game of Texas Hold’Em with 2 cards dealt and additional 5 cards on the table shared by all players.

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