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3. Three men and three women were nominated for THREE positions on the school board. Suppose the three male are named A, B, and C, and the female are named D, E, and F. Further, suppose that the following statements are true: • There should be at least one male and at least one female to be selected; • If A won a position, so did D; . If neither C nor F won a position, then E did not win a position; If A did not win a position, then both D and E won positions; • C cannot be the only male candidate to be selected; Either E or F (or both) would win a position. There is only one way to choose three candidates to satisfy all criteria above. Please find that way and justify it to be the only valid choice.

3. Three men and three women were nominated for THREE positions on the school board. Suppose the three male are named A, B, and C, and the female are named D, E, and F. Further, suppose that the following statements are true: • There should be at least one male and at least one female to be selected; • If A won a position, so did D; . If neither C nor F won a position, then E did not win a position; If A did not win a position, then both D and E won positions; • C cannot be the only male candidate to be selected; Either E or F (or both) would win a position. There is only one way to choose three candidates to satisfy all criteria above. Please find that way and justify it to be the only valid choice.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. Three men and three women were nominated for THREE positions on the school board. Suppose the three male are named A, B, and C, and the female are named D, E, and F. Further, suppose that the following statements are true: • There should be at least one male and at least one female to be selected; If A won a position, so did D; • If neither C nor F won a position, then E did not win a position; If A did not win a position, then both D and E won positions; • C cannot be the only male candidate to be selected; • Either E or F (or both) would win a position. There is only one way to choose three candidates to satisfy all criteria above. Please find that way and justify it to be the only valid choice.
Transcribed Image Text:3. Three men and three women were nominated for THREE positions on the school board. Suppose the three male are named A, B, and C, and the female are named D, E, and F. Further, suppose that the following statements are true: • There should be at least one male and at least one female to be selected; If A won a position, so did D; • If neither C nor F won a position, then E did not win a position; If A did not win a position, then both D and E won positions; • C cannot be the only male candidate to be selected; • Either E or F (or both) would win a position. There is only one way to choose three candidates to satisfy all criteria above. Please find that way and justify it to be the only valid choice.
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