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Discrete Mathematics with Graph Theory (3rd Edition) 192

# Discrete Mathematics with Graph Theory (3rd Edition) 192 -...

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190 Solutions to Exercises 5. [BB] (a) (b) (~) _ 15. M - 64' (c) 1 + (~) + (~) _ 11. 64 - 32' 6. (a) (d) (d) 1 1 _ 63. -64-64' 1 + G) 1 ~=16 (b) (e) (~) + (~) + (~) - 1 64 - 2' (e) G)=~ 128 128 (i)+G)+G)+G) _1 128 - 2" (c) 1 1 + (i) _ 15. -~-16' 7. [BB] (a) There are (~) outcomes in the sample space. For an outcome to be in the event described, we need to choose three from the six selected numbers and three from the 43 other numbers. The answer l 'S m (~) ~ 0 018 (~) ~. . 1 (c) 1 - (~) ~ 1.000. 9. [BB] (a) 1~~~~) = i; (b) 1- i =~; (c) 1- l~f~~) =~; (d) ;1W~? = 1 5 8; (e) We will use the formula given in part (3) of Theorem 7.3.2. Let A be the event "at least one white ball" and B be "exactly one red ball." We saw in (c) that P(A) = ~. Also P(B) = ;Wg? = ~~. Since An B is the event described in (d), P(A n B) = 1 5 8' The required probability is P{A U B) = 5 35 5 55 9" + 72 - 18 = 72' 10 () 3(3) _ 1 . . a 12(12) - 16' (b) 1 1 - 15. - 16 - 16' ( ) 1 9(9) _ 7. C - 12(12) - 16' ( d) 2(3)(4) = 12('12) 6' (e) Let
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