Explanation Definition: The Fundamental Counting Principle (FCP): If we want to perform a series of tasks and the first task can be done in a ways, the second can be done in b ways, the third can be done in c ways, and so on, then all the tasks can be done in a × b × c … ways. Calculation: Given, We assume that we are drawing five cards from a standard 52-card deck that contain two diamonds and three hearts. Since a deck of 52 cards has 13 cards of diamond and 13 cards of heart, two cards of diamond can be chosen in 13 C 2 and three cards of heart can be drawn at 13 C 3 . Using the formula for combination, C ( n , r ) = n ! r ! ( n − r ) ! Here, n = 13 and r = 2 C ( 13 , 2 ) = 13 ! 2 ! ( 13 − 2 ) ! C ( 13 , 2 ) = 13 ! 2 ! 11 ! C ( 13 , 2 ) = 13 ⋅ 12 ⋅ 11 ! 2 ! 11 ! C ( 13 , 2 ) = 13 ⋅ 12 2 ⋅ 1 C ( 13 , 2 ) = 156

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ISBN: 9780135902783

Author: Pirnot

Publisher: PEARSON

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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Chapter 12.3, Problem 79E

To determine

The number of ways that we can choose a five-card hand from a standard deck that contains two diamonds and three hearts.

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Chapter 12.3, Problem 78E

Chapter 12.3, Problem 80E

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The number of ways that we can choose a five-card hand from a standard deck that contains two diamonds and three hearts.

Solution Summary: The author calculates the number of ways that a five-card hand can be drawn, based on the Fundamental Counting Principle.

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The number of ways that we can choose a five-card hand from a standard deck that contains two diamonds and three hearts.

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Chapter 12 Solutions