Discrete Mathematics with Graph Theory (3rd Edition) 203

Discrete Mathematics with Graph Theory (3rd Edition) 203 -...

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Unformatted text preview: Section 7.6 7' (1 - .1. + .1. - .1. + .1. _ .1. + .1. _ .1.) . I! 2! 3! 4! 5! 6! 7! 7! - 7! + 7 . 6 . 5 . 4 . 3 - 7 . 6 . 5 . 4 + 7 . 6 . 5 - 7 . 6 + 7 - 1 2520 - 840 + 210 - 42 + 6 = 1854 Ds 8' (1 - .1. + .1. _ .1. + .1. _ .1. + .1. _ .1. + .1.) . I! 2! 3! 4! 5! 6! 7! S! 8! - 8! + 8 . 7 . 6 . 5 . 4 . 3 - 8 . 7 . 6 . 5 . 4 + 8 . 7 . 6 . 5 - 8 . 7 . 6 +8 7 - 8 + 1 = 20,160 - 6720 + 1680 - 336 + 56 - 7 = 14,833 2. This is D 26 = 26!(1- fr + tr --lr + ... + 2~!)' 3. [BB] This is Dn = 11!(1 - fr + -ft --lr + ... - 1~!)' 4. D50 5. (a) D7 6. (a) D 20 (b) [BB] 7! - D7 (b) 20! - D20 (c) 1 201 (c) [BB] There are 20 choices for the person who receives his or her own hat. For each choice, the 19 other people can get their hats in D 19 ways. Hence, the answer is 20D19. (d) This is the answer to (b) less the answer to (c); that is, 20! - D20 - 20D19. (e) This means either no person receives hislher own hat or exactly one person receives hislher own hat or exactly two people receive their own hats. The answer is hat or exactly two people receive their own hats....
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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