184a_01w_fe

# 184a_01w_fe - Math 184A Final Exam(200 points March 2001...

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Unformatted text preview: Math 184A Final Exam (200 points) March 2001 • Please put your name and ID number on your exam. If you are not using a blue book, put your name on every page. • The exam is CLOSED BOOK, but ONE SHEET of notes is allowed. • You must show your work to receive credit. 1. (30 pts) We want to divide 6 men and 7 women into two teams of 6 people each, plus one referee. (a) How many ways can this be done if the teams have no names? (b) How many ways can this be done if one team is called the “Hackers”, the other is called the (Number) “Crunchers”, and each team must have 3 women and 3 men? 2. (20 pts) Suppose a = 0, a 1 = 1 and a n +1 = 2 a n- a n- 1 + 6 n for n ≥ 1. Find a simple formula for a n (not a recursion) and prove it by induction. Hint : Compute the first few values of a n and look for a pattern. 3. (15 pts) Suppose n > 1 Imagine listing the n ! permutations of { 1 , 2 , . . . , n } in direct insertion order. What permutation has rank n ! / 2? Be sure to explain how you got...
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184a_01w_fe - Math 184A Final Exam(200 points March 2001...

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