Explanation Given: The president of a large company selects six employees to receive a special bonus. He claims that the six employees are chosen randomly from among the 30 employees, of whom 19 are women and 11 are men. Approach: Combinations: Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. Formula used: C n r = n ! r ! ( n − r ) ! … ( 1 ) Here, n is the total number of items and r is the number of items being chosen at a time. If E is the event in a sample space S , then the probability of E is P ( E ) = n ( E ) n ( S ) … ( 2 ) Calculation: There are 30 employees in company. So, n = 30 Six employees are selected at random. So, the number of possible outcomes is, n ( S ) = C 30 6 Substitute 30 for n and 6 for r in equation ( 1 ) . C 30 6 = 30 ! 6 ! ( 30 − 6 ) ! = 30 ! 6 ! 24 ! Now, n ( S ) = 30 ! 6 ! 24 ! There are 19 are women and 11 are men

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 14.2, Problem 46E

To determine

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The probability that no woman is chosen.

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Chapter 14.2, Problem 45E

Chapter 14.2, Problem 47E

Chapter 14 Solutions

Algebra and Trigonometry (MindTap Course List)

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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To find: The probability that no woman is chosen.

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To find:

The probability that no woman is chosen.