Explanation 1) 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. 2) Calculation: Given, The president of your college has asked the president of student government to form an eight-person presidential advisory committee from among 17 student leaders. For find the number of ways, we follow the below three stages Stage 1: The number of ways to choose one chair of committee among 17 student leaders. (i.e.) P ( 17 , 1 ) Stage 2: The number of ways to select two others Co-facilitators of remaining student leaders. (i.e.) C ( 16 , 2 ) Stage 3: The number of ways to select others five on the committee will have no special roles. (i.e.) C ( 14 , 5 ) Thus, we can apply for the fundamental counting principle. Stage 1: C ( 17 , 1 ) Using the formula for permutations, P ( n , r ) = n ! ( n − r ) ! Here, n = 17 and r = 1 P ( 17 , 1 ) = 17 ! ( 17 − 1 ) ! P ( 17 , 1 ) = 17 ! 16 ! P ( 17 , 1 ) = 17 ⋅ 16 ! 16 ! P ( 17 , 1 ) = 17 ways. Stage 2: C ( 16 , 2 ) Using the formula for combination, C ( n , r ) = n ! r ! ( n − r ) ! Here, n = 16 and r = 2 C ( 16 , 2 ) = 16 ! 2 ! ( 16 − 2 ) ! C ( 16 , 2 ) =

Mathematics All Around, Books a la carte edition (6th Edition)

6th Edition

ISBN: 9780134462448

Author: Pirnot, Tom

Publisher: PEARSON

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…

Counting Theory

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 70E

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The number of ways to form an eight person presidential advisory committee among 17 student leaders.

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Chapter 12.3, Problem 69E

Chapter 12.3, Problem 71E

Chapter 12 Solutions

Mathematics All Around, Books a la carte edition (6th Edition)

Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - In Exercises 14, you are selecting from the set...Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - How many different two-digit numbers can you form...Ch. 12.1 - How many different two-digit numbers can you form...

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To find:

The number of ways to form an eight person presidential advisory committee among 17 student leaders.