ABSTRACT
Many problems in mathematics, computer science, and engineering involve counting objects with particular properties. Although there are no absolute rules that can be used to solve all counting problems, many counting problems that occur frequently can be solved using a few basic rules together with a few important counting techniques. This chapter provides information on how many standard counting problems are solved. Most counting methods are based directly or indirectly on the fundamental principles and techniques. The rules of sum, product, and quotient are the most basic and are applied more often than any other. The chapter includes some applications of the pigeonhole principle, a brief introduction to generating functions, and several examples illustrating the use of tree diagrams and Venn diagrams. A tree diagram is a line-drawing of a tree, often with its branches and/or nodes labelled.
