Discrete Mathematics and Combinatorics

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 ...