quiz3-1 - EECS 310 - Fall 2009: Quiz #3 Instructor: Nicole...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
EECS 310 - Fall 2009: Quiz #3 Instructor: Nicole Immorlica Date: Nov 24, 2009 Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. You must answer all questions. Name: 1. (20 points) Combinatorics. (a) (10 points) Give a combinatorial proof of the fact that ( n k ) = n k ( n - 1 k - 1 ) . That is, explain why the right-hand side counts the number of ways to select k elements from a set of n . (b) (10 points) How many sequences are there of the integers { 1 ,...,n } such that 1 appears before 2? (123 ...n and 345 ...n 12 are examples.) You may leave your answer in combination or permutation form, but your answer must be in closed form (i.e., no summations).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. (20 points) Probability. Let n be an even integer. Suppose you have a sack with n balls numbered { 1 ,...,n } . Compute the following. You may leave your answer in combination or permutation form, but your answer must be in closed form (i.e., no summations).
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/15/2012 for the course ECON 101 taught by Professor N/a during the Fall '11 term at Middlesex CC.

Page1 / 5

quiz3-1 - EECS 310 - Fall 2009: Quiz #3 Instructor: Nicole...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online