ABSTRACT
This chapter introduces one of the most basic tools of counting and starts with an example. One application of counting is to compute probabilities. In the insurance industry, actuaries study the probabilities of accidents or deaths to determine insurance premiums. Overcounting is at the heart of the Basic Inclusion–Exclusion Principle. The Addition Principle is simply the special case of the Basic Inclusion–Exclusion Principle. The chapter focuses on problems to which the Multiplication Principle does apply. A better appreciation for the Multiplication Principle can be gained by considering an example in which it does not apply. By using factorials, permutations, and combinations as the basic building blocks and the multiplication and addition principles as the tools for assembling these blocks, people are able to build up to solving more and more complex enumeration problems. The chapter explores the applications of combinations.
