A Combinatorial Application of Linear Algebra

The purpose of this paper is to present an application that I have used many times while teaching an introductory course in linear algebra. This application deals with an occupancydistribution problem which is simple to state and easy to understand. I present the problem on the first day of classes and I encourage the students to work on it. I also tell the class that I will provide a solution later based upon some of the topics to be discussed during the course. Generally, students have found this a very difficult problem to solve and they have appreciated the solution when it is eventually presented in class.