Discrete Mathematics with Graph Theory (3rd Edition) 201

Discrete Mathematics with Graph Theory (3rd Edition) 201 -...

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Section 7.5 199 9. (a) There are e50) ways for Philadelphia to select its players and then C5 5 ) ways for Boston to choose, then C50) ways for Miami, after which Toronto's players are detennined. The answer is e50) C5 5 ) C~) = 5!;!~!!5! = 11,732,745,024. (b) Each answer to this question gives rise to 4! answers to part (a) since for each division into four teams, there are 4! ways to assign them to four different cities. So the answer here is 5!5F5~k!4! = 488,864,376. 10. There are C6 2 ) ways in which San Diego can choose its players, then (~) ways for Houston to choose, after which Toronto gets the remaining two players. By the multiplication rule, there are altogether C6 2 ) m = 924(15) = 13860 possible drafts. 11. (a) [BB] Select the boxes for the red balls in one of (~g) ways, then the boxes for the white balls in one of (~g) ways and finally the boxes for the blue balls in one of (ig) ways. The answer is ( 60) (50) (40) 60! 10
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