This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: exams have been returned in lecture. SIGN HERE: . Problem Points Score 1 35 2 35 3 30 Total 100 1. (35) Suppose that m, n 5. How many northeastern lattice paths are there from the point (0 , 0) to the point ( m, n ) which begin by going up, go through the point (4 , 2), and do not go through the point (4 , 5)? 1 2. (35) This problem has two parts. a. Prove that n k + n k + 1 = n + 1 k + 1 for all nonnegative integers n and k . b. Prove that n k =0 k n k = n 2 n1 for all nonnegative integers n . 2 3. (30) A student has 37 days to write her thesis and she knows that it will take exactly 60 hours of work. Each day she works for a positive integer number of hours. a. How many diFerent possible schedules are there? b. Prove that no matter what schedule she chooses, there will be a succession of days during which she will have worked exactly 13 hours. 3 4...
View
Full
Document
This note was uploaded on 12/10/2011 for the course MAD 4203 taught by Professor Vetter during the Fall '10 term at University of Florida.
 Fall '10
 Vetter

Click to edit the document details