CMPSCI 250: Introduction to Computation

David Mix Barrington

Fall, 2004

CMPSCI 250 Practice Midterm #3

Posted 14 November 2004

Actual midterm will be 18 November 2004

There are four questions for 100 total points.

Question 3(c) corrected 16 November.

When your answer to a problem is a particular number, you may use exponents, falling exponents, factorials, and/or the "choose" notation to indicate the number. However, if the answer is less than 100, you must give the number in ordinary decimal notation for full credit.

Question 1 (20):

A sushi bar sells five kinds of rolls: Alaska, California, Eel, Salmon, and Tuna. Six customers enter the bar and order one roll each.

Question 2 (30): Let n and k be arbitrary positive naturals with k ≤ n.

Question 3 (30): If n and k are any naturals, define h(n,k) to be the number of subsets of the set {1,...,n} of size k that do not contain two adjacent numbers. For example, h(4,2) = 3 because the relevant sets are {1,3}, {1,4}, and {2,4}. The other three subsets of size 2 contain two adjacent numbers.

Question 4 (20): The word "CAMBRIDGE" consists of nine different letters.

Last modified 16 November 2004