Explanation Given information: There are 30 candidates in a pool and a board of directors of eight members can be chosen in such a way that there is a chairman,a treasurer, a secretary and five other members. Concept used: Fundamental Counting Principle: Suppose two events occur in order. If the first event can occur in p ways and the second event can occur in q ways, then the two events can occur in order in p × q ways. Formula used: The formula to calculate the number of combinations of n objects takes r at a time is, C ( n , r ) = n ! r ! ( n − r ) ! ...... (1) Calculation: It is given that there are 30 candidates in a pool and a board of directors of eight members can be chosen in such a way that there is a chairman,a treasurer, a secretary and five other members. Substitute 30 for n and 1 for r in equation (1) to obtain the number of wayssuch that one chairman can be chosen from 30 candidates as follows, C ( 30 , 1 ) = 30 ! 1 ! ( 30 − 1 ) ! = 30 ! 1 ! 29 ! = 30 ⋅ 29 ! 29 ! = 30 Now, there are 29 candidates left. Substitute 29 for n and 1 for r in equation (1) to obtain the number of wayssuch that one treasurer can be picked from 29 candidates as follows, C ( 29 , 1 ) = 29 ! 1 ! ( 29 − 1 ) ! = 29 ! 28 ! = 29 ⋅ 28 ! 28 ! = 29 Now, there are 28 candidates left. Substitute 28 for n and 1 for r in equation (1) to obtain the number of wayssuch that one secretary can be chosen from 28 candidates as follows, C ( 28 , 1 ) = 28 ! 1 ! ( 28 − 1 ) ! = 28 ! 27 ! = 28 ⋅ 27 ! 27 ! = 28 Now, there are 27 candidates left

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ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 9, Problem 8T

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The different number of ways such that a board of directors of eight members can be chosen from a pool of 30 candidates and the board of directors is to consist of a chairman, a treasurer, a secretary and five other members.

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Chapter 9, Problem 7T

Chapter 9, Problem 9T

Chapter 9 Solutions

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Ch. 9.1 - The Fundamental Counting Principle says that if...Ch. 9.1 - The number of ways of arranging r objects form n...Ch. 9.1 - The number of ways of choosing r objects from n...Ch. 9.1 - True or False? In counting combinations, order...Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Evaluating Permutations and Combinations Evaluate...

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The different number of ways such that a board of directors of eight members can be chosen from a pool of 30 candidates and the board of directors is to consist of a chairman, a treasurer, a secretary and five other members.

Solution Summary: The author calculates the number of ways a board of directors of eight members can be chosen from the pool of 30 candidates.

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To find: The different number of ways such that a board of directors of eight members can be chosen from a pool of 30 candidates and the board of directors is to consist of a chairman, a treasurer, a secretary and five other members.

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Chapter 9 Solutions

To find:

The different number of ways such that a board of directors of eight members can be chosen from a pool of 30 candidates and the board of directors is to consist of a chairman, a treasurer, a secretary and five other members.