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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 fivecard hands contain one pair, but not two pair or 3 of a kind? 2. (12 pts.) Find the 6leaf, unlabeled, binary RPtree whose rank among all such 6leaf 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 RPtrees in which each vertex has an even number of downward edges (and, of course, one upward edge if it is not the root). I’ll 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
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 Math, Recursion, pts, Tower of Hanoi, standard Tower

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