Explanation Given: In the group of 30 contestants, six are selected as semifinalists, two are selected as finalists, and then one finalist is awarded by the top prize. Approach: Fundamental counting principle says that when r objects are selected out of n objects and the order of selection does not matter, then use combination. The number of combinations of n distinct objects taken r at a time is, C ( n , r ) = n ! r ! ( n − r ) ! ; ( r ≤ n ) . Calculation: First, as the order does not matter in the selection of semifinalists, the number of ways of the selection are given by, C ( 30 , 6 ) . After selecting the semifinalists, the number of ways of selecting two finalists is given as, C ( 6 , 2 ) . After that the number of ways of awarding the prize to one finalist is given as, C ( 2 , 1 )

4th Edition

ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Chapter 14.1, Problem 89E

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The number of ways of awarding the top prize to the finalist in a sequence.

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Chapter 14.1, Problem 88E

Chapter 14.1, Problem 90E

Chapter 14 Solutions

Algebra and Trigonometry

Ch. 14.1 - CONCEPTS The Fundamental Counting Principle says...Ch. 14.1 - CONCEPTS The number of ways of arranging r objects...Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Prob. 10E

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The number of ways of awarding the top prize to the finalist in a sequence.

Solution Summary: The author explains that the number of ways of awarding the top prize to the finalist in a sequence is 17,813,250.

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To find: The number of ways of awarding the top prize to the finalist in a sequence.

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Chapter 14 Solutions

To find:

The number of ways of awarding the top prize to the finalist in a sequence.