Page 163 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II Richa Nandra, Lovely Professional University

Notes Unit 12: Permutation

CONTENTS
Objectives
Introduction

12.1 Multiplication and Addition Principles
12.2 Factorial
12.3 Permutations

12.4 Circular Permutation
12.5 Summary
12.6 Keywords
12.7 Review Questions
12.8 Further Readings

Objectives

After studying this unit, you will be able to:
 Understand the concept of Permutation

 Understand the circular permutation
 Discuss the factorial
Introduction

Permutation is the method of arrangement of things. The expression arrangement is used, if the
order of things is measured. A permutation is defined as an arrangement of a group of objects in
a specific order. In this unit, you will understand various concepts of permutation such as
factorials, circular permutation, etc.

12.1 Multiplication and Addition Principles

Let us start with considering the following situation: Suppose a shop sells six styles of pants.
Each style is available in 8 lengths, six waist sizes, and four colours. How many different kinds
of pants does the shop need to stock?
There are 6 possible types of pants; then for each type, there are 8 possible length sizes; for each
of these, there are 6 possible waist sizes; and each of these is available in 4 different colours. So,
if you sit down to count all the possibilities, you will find a huge number, and may even miss
some out! However, if you apply the multiplication principle, you will have the answer.

So, what is the multiplication principle? There are various ways of explaining this principle.
One way is the following:
Suppose that a task/procedure consists of a sequence of subtasks or steps, say, Subtask 1, Subtask
2,…, Subtask k. Furthermore, suppose that Subtask 1 can be performed in n , ways, Subtask 2 can
1
be performed in n ways after Subtask 1 has been performed, Subtask 3 can be performed in n
2 3

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