final exam - Math 55, Final Exam Wednesday, May 20,...

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Unformatted text preview: Math 55, Final Exam Wednesday, May 20, 8:00am11:00am This exam is closed book. Do not use any books, notes or electronic devices. Please write in a blue note book, with your name, the name of your TA and your section time on the front. Each of the 10 problems is worth 10 points, for a total of 100 points. Answers without justification will receive no credit. (1) (a) How many nonisomorphic unrooted trees are there with 4 vertices ? (b) How many nonisomorphic rooted trees are there with 4 vertices ? (2) How many ways are there to distribute five balls into three boxes if each box must have at least one ball in it and (a) the balls are labeled but the boxes are unlabeled? (b) the balls are unlabeled but the boxes are labeled? (c) both the balls and the boxes are unlabled? (3) Give a recursive definition of the set of bit strings that are palindromes. (4) Consider the divisibility poset ( { 1 , 2 , 3 , 12 , 18 , 36 } , | ) ....
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final exam - Math 55, Final Exam Wednesday, May 20,...

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