The Theory of Counting

Abstract

The theory of counting, or enumeration, is the theoretical counterpart of everyday practical counting. The chapter starts by defining an experiment to be any activity with well-defined, observable outcomes or results, and an event as a set of outcomes. Tree diagrams are introduced to represent sequences of events.

The multiplication principle and the rule of sum are introduced. Venn diagrams are used to describe events and in counting the number of outcomes in unions and intersections of events. The principle of inclusion and exclusion is introduced.

One-to-one correspondences are discussed, as are finite and infinite and countable and uncountable sets. Selections and arrangements are studied, leading to the binomial theorem.