15b_01f_qe

15b_01f_qe - 15B Weekly Quizzes Fall 2001 You may leave...

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15B Weekly Quizzes Fall 2001 You may leave sums, products, factorials, binomial coefficients, and so on in your answers. Q1. A family has 3 girls and 3 boys. Give reasons for your answers. (a) How many ways can they sit around a circular table? (b) How many ways can they sit in a row if girls and boys must alternate; that is, two boys cannot sit next to each other and two girls cannot sit next to each other? Q2. Homework problems CL-3.1 (3 pair in 6 cards) and CL-3.2 (straight). Q3. Let A = { 1 , 2 , 3 } and B = { 1 , 2 , 3 , 4 , 5 } . A function is chosen uniformly at random from B A . (a) What is the probability that it is an injection? (b) What is the probability that it is a surjection? To receive credit, be sure to show how you got your answers. Q4. Here is a permutation f in cycle form: (1 , 6 , 3 , 2) (4 , 7 , 5). (a) Write f in one-line form. (b) Write f - 1 in cycle form. (c) Write f 13 in cycle form. Q5. Given that
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This note was uploaded on 06/17/2009 for the course MATH 15B taught by Professor Bender during the Fall '01 term at UCSD.

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15b_01f_qe - 15B Weekly Quizzes Fall 2001 You may leave...

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