# NCERT Exemplar Class 11 Maths Chapter 7 Solutions: Permutations and Combinations

NCERT Exemplar Solutions for Class 11 Maths Chapter 7 will introduce you to a few basic and advanced techniques, which will let you define the various ways of arranging and choosing objects. The problems of this chapter are completely based on the important principle of counting. It is one of the easiest chapters featured in the NCERT Exemplar Class 11 Maths syllabus.

The important topics of Chapter 7 – Permutations and Combinations include the fundamental principle of counting, permutations, combinations, factorial notation, addition principle, multiplication principle, and theorems based on permutations and combinations. The chapter consists of properties of Permutations and Combinations and some important formulae.

The chapter of NCERT Exemplar Solutions for Class 11 Maths contains 3 main exercises with a total of 83 questions. All the exercises have different types of questions available which in turn will help to prepare for the exams well. You can follow the solutions provided by the expert maths teachers at Instasolv for your better understanding of the concepts.

## Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 7 – Permutations and Combinations

**What are Permutations?**

The total number of permutations of n different things taken r at a time, where repetition is not permitted, is represented by ^{n}Pr and is given by ^{n}P_{r} = n!/ (n – r)!

where 0 ≤ r ≤ n

n! = 1 x 2 x 3 x 4 x … x n

n! = n x (n – 1)!

**What are Combinations?**

The number of combinations of n various things taken r at a time, denoted by ^{n}C_{r} is given by ^{n}C_{r} = n!/ r! (n – r)!, 0 ≤r ≤ n.

**Addition Law**

If there are two statements such that they can be executed individually in m and n ways respectively, then either of the two statements can be executed in (m + n) ways.

**Multiplication Law**

If one statement can be executed in m ways and if equivalent to each of the m ways of executing this operation, there are n ways of executing a second statement, then the number of ways of executing two operations together in (m x n).

**Factorial Notation**

The sustained product of first n natural numbers is known as the ‘n factorial’ and is represented by n!.

### Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 7 – Permutations and Combinations

This chapter of NCERT Exemplar Solutions for Maths Class 11 consists of 19 solved examples for your reference to practice the exercises with ease. Other than this, there are 3 main exercises in the chapter. It has a total of around 83 questions. The detailed description of all these exercises are listed below:

**Exercise 7.1 – Short Answer Type Questions**

In this exercise of Chapter 7 – Permutations and Combinations there are a total of 20 questions that are based on the concepts of arranging and choosing objects.

**Exercise 7.2 – Long Answer Type Questions**

NCERT Maths Exemplar Solutions Class 11 Chapter 7 Exercise 7.2 contains a total of 5 questions. They are long answer type questions where you have to find the fundamental principle of counting, permutations, combinations, and factorial notation. There are also questions related to the addition principle and multiplication principle.

**Exercise 7.3 – Objective Type Questions**

This exercise consists of a total of 39 questions which are objective type questions based on properties of permutations and combinations and some important formulae. This exercise includes MCQs, fill in the blanks, match the following and state true or false type questions.

## Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 7 – Permutations and Combinations by Instasolv?

- NCERT Maths Exemplar Solutions for Class 11 Chapter 7 – Permutation and Combinations provided by Instasolv are important for thorough learning of the chapter.
- These solutions are a highly beneficial contribution to the success of not only your academic exams but also to prepare for the entrance exams like JEE.
- Solving difficult problems in Chapter 7 with the help of these solutions will help you initiate new ways of solving the questions with different techniques.
- Referring to NCERT Exemplar Class 11 will help you make sure that you do not miss any important questions during the preparation of your exams.
- All the solutions are prepared by the experts of Instasolv to help you clear your doubts without going anywhere else.