CMPSCI 250: Introduction to Computation

David Mix Barrington

Fall, 2004

CMPSCI 250 Solutions to Practice Midterm #3

Exam posted 14 November 2004

Solutions posted 16 November 2004

Actual midterm will be 18 November 2004

There are four questions for 100 total points.

Solutions are in blue.

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