## Chapter 4

## Counting Principles

#### Learning Objectives

On completing this chapter, you should be able to:

state the fundamental counting principle

distinguish between permutations and combinations

identify and solve problems involving the use of fundamental counting principle, permutations and combinations

understand the idea of a circular permutation and state the formula for the number of all circular permutations of *n* objects

identify and solve problems based on permutation of identical objects

state and prove the multi-nomial theorem

solve problems based on distribution of identical objects, which include problems on compositions of a positive integer

##### 4.1 A FUNDAMENTAL COUNTING PRINCIPLE

Let us think of a simple password consisting of just ...