# Introduction

What can be the maximum population of a country in which no two persons have identical set of teeth? In how many ways can we attempt 5 questions from a question paper containing 7 questions? In how many ways can 5 students be arranged to speak at a function? These are some of the questions which we shall be able to answer by learning the techniques given in this chapter.

The word permutation means all possible ways of arrangements.

The permutation of a number of objects is the number of different ways of arranging the objects. In permutation the position of the chosen object is also important.

For example, let us consider two pictures A and B. How many possible ways of hanging the pictures are possible?

There are only 2 possible ways of hanging them. The two patterns for hanging the pictures are shown below:
The various ways in which objects are selected from a set may be, generally without replacement, to form subsets.

With combinations, on the other hand, one does not consider the order in which objects were chosen or placed, just which objects were chosen.

Difference between permutation and combination is given as follows