COMP 2804 Midterm: COMP 2804 Midterm 1 Fall 2014

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October 24, 2014: all questions must be answered on the scantron sheet, write your name and student number on the scantron sheet, you do not have to hand in this examination paper. Marking scheme: each of the 17 questions is worth 1 mark: newton: (x + y)n = pn k=0 (cid:0)n k(cid:1)xn kyk. 1: let n 2 be an integer. How many bitstrings of length n are there that contain at least two 1s? (a) (cid:0)n. How many ways are there to arrange them on a line if all boys are standing next to each other and all girls are standing next to each other. (a) 17! )2: consider 12 boys, 17 girls, and 25 dogs. In any group of 900 people, there must be at least three people that have the same birthday. (a) true (b) false: consider a square with sides of length 3. 80 (cid:1)520380 (a) (cid:0)100 (b) (cid:0)100 (c) (cid:0)100 (d) (cid:0) 80.

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