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Discrete Mathematics with Graph Theory (3rd Edition) 189

Discrete Mathematics with Graph Theory (3rd Edition) 189 -...

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Section 7.2 187 (c) [BB] Choose the red balls in C3 5 ) ways and then the white balls in C20) ways. The answer is (~) C~) = 20,475. 12. (a) m = 56 (b) Choose the mathematicians in m ways and then the geologists in m ways. The answer is mm = 10(3) = 30. (d) [BB] Choose the five cars to undergo each of the tests, then choose 15 from the remaining 95 for the first test and 15 from the available 80 for the second test. The answer is C~O) x (~~) x (~~). This is also C2000) e~) (~~). (Why?) 14. (a) (~) = 3060; (c) C:) = 18564. 15. (a) m = 84 (b) The number of groups which include the divorced couple is m. Thus, the number in which not both of these people are present is (~) - m = 84 - 35 = 49. (c) Our hostess must either invite two married couples and two singles or all three married couples. The answer is m m + 1 = 10. 16. (a) e5 2 ) = 26334 (b) The total number of committees is (25 2 ). The number of committees which contain no statistician is C;), so the number which contain at least one is (25 2 ) - C;) = 26334 - 11628 = 14706. (c) The total number
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