hw08sol - Math 55: Discrete Mathematics, Fall 2008 Homework...

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Math 55: Discrete Mathematics, Fall 2008 Homework 8 Solutions *[3,3 and 4 points] 5.5: 10(a) ( 12+6 - 1 12 ) (choosing 12 things from 6 with repetitions) (c) ( 12+6 - 1 12 ) (the first two of each kind make 12 and you have a dozen left to choose freely) (f) ( 15+6 - 1 15 ) - ( 11+6 - 1 11 ) (count choices without any restriction on broccoli, then subtract those with at least 4 broccoli) 34. ( 5 3 , 2 ) + ( 5 3 , 1 , 1 ) + ( 5 2 , 3 ) + ( 5 2 , 2 , 1 ) + ( 5 1 , 3 , 1 ) + ( 6 3 , 3 ) + ( 6 3 , 2 , 1 ) + ( 6 2 , 3 , 1 ) + ( 7 3 , 3 , 1 ) (one term for each possible number of E’s, S’s and R’s adding up to at least 5) 42. ( 52 13 , 13 , 13 , 13 ) = 52! / (13!) 4 6.1: 8. ( 51 4 ) / ( 52 5 ) 16. 4 ( 13 5 ) / ( 52 5 ) 18. 4 · 10 / ( 52 5 ) 30. 6 · 34 / ( 40 6 ) (I assume that the problem intends an unordered subset of 6 integers chosen at random from { 1 ,..., 40 } . The numerator counts subsets that match exactly 5 of the player’s chosen 6.) 36. 8 is more likely with two dice than three. With two dice,
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hw08sol - Math 55: Discrete Mathematics, Fall 2008 Homework...

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