Discrete Mathematics with Graph Theory (3rd Edition) 215

Discrete Mathematics with Graph Theory (3rd Edition) 215 -...

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Unformatted text preview: Chapter 7 213 C50) m = 2520 groups of 2, 3 and 5; ~ (~O) (~) = 1575 groups of 2, 4 and 4; and ~ (~) (~) = 2100 groups of 3, 3 and 4. By the addition rule, 630 + 2520 + 1575 + 2100 = 6825 groups can be formed. 11. She can purchase the books in C;) ways. For each of these purchases, there are three possibilities. In Case 1, one boy friend receives 4 books and each of the other boys just one. There are 5 x (!) x 4! = 8400 ways this can occur. In Case 2, one boy receives three books, one boy receives two and three boys receive one each. There are 5 x 4 x (~) x @ x 3! = 67200 ways in which this can occur. In Case 3, three boys each receive two books and two each receive one book. This can occur in (~) x m x (~) x @ x 2! = 50400 ways. The answer is (~2) (8400+67200+50400) = 495 x 126,000 = 6,237,000. 12. Seat the Israeli delegation at the table first. There are 4 choices for the delegation to the right of Israel and then 3 for the delegation to the left. This leaves 7 delegations which can be seated in 7! ways. The and then 3 for the delegation to the left....
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