203w07hw9 - requirements • There are at most 6 yellow...

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EECS 203, Discrete Mathematics Winter 2007, University of Michigan, Ann Arbor Problem Set 9 Problems from the Textbook 5.4 14[E], 22[E], 30[M] 5.5 16[M], 30[E], 46[M], 62[E] * Additional Problems Required for All Students Problem A9.1 (E). Let n 0 be an integer. Prove the following identity 1 n + 1 2 n +1 - 1 = n i =0 n i 1 i + 1 . Problem A9.2 (C). Let n 1 be an integer and A be a set of n elements. Suppose f, g : 2 A R satisfy f ( x ) = y : x y A g ( y ) , x A. Prove that g ( y ) = x : y x A ( - 1) | x - y | f ( x ) , x A. * Extra Credit Problem A9.3. Cecilia goes to the florist to order 100 flowers for a special event. She has the following
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Unformatted text preview: requirements: • There are at most 6 yellow tulips and at most 6 purple tulips. • The number of orchids is a multiple of 5. • There are at most 4 lilies. • The number of roses must be a multiple of 7. Each is either red or blue, but at most 1 / 7 of them are blue. In how many combinations she can order the flowers? 1...
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