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Unformatted text preview: Math 184A Final Exam Fall 2002 Please put your name and ID number on your blue book. The exam is CLOSED BOOK. You may have TWO PAGES of notes plus the sheet of principles. Calculators are NOT allowed. You must show your work to receive credit. 1. (12 pts.) How many five-card hands contain one pair, but not two pair or 3 of a kind? 2. (12 pts.) Find the 6-leaf, unlabeled, binary RP-tree whose rank among all such 6-leaf trees is 22. b 1 = b 2 = 1 b 3 = 2 b 4 = 5 b 5 = 14 b 6 = 42 3. (24 pts.) Consider unlabled RP-trees in which each vertex has an even number of downward edges (and, of course, one upward edge if it is not the root). Ill draw some pictures on the board. Let t n be the number of such trees with n vertices and let T ( x ) be the generating function t n x n . (a) Derive the formula T ( x ) 3- T ( x ) + x = 0. (b) It can be shown that t n An B C n for some constants A , B and C . Find B and C ....
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- Fall '08