NCERT solutions for class 11 maths chapter 7 are prepared as per the CBSE guidelines. Permutation is defined as several possible for arranging a set or number of things. The expression to denote permutation is ^{n}P_{r}. Combinations means the selection of all or part of a set of objects, irrespective of the order in which objects are selected.

There are four exercises & a miscellaneous exercise in this chapter that assists the students to understand the concepts related to Permutations and Combinations clearly.

Table of Contents

## NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination

The students learn about the Permutation and Combination in detail that enables them to score full marks from this chapter by practicing the solutions for all the problems available in the NCERT textbook. The students can conveniently download NCERT solutions for class 11 maths chapter 7 PDF that also boosts their confidence and reduces their fear of final examination.

NCERT class 11 maths chapter 7 solutions are prepared by the subject experts & cover all the exercise questions included in the NCERT textbook. These solutions assist the students while doing their homework.

You can download CBSE NCERT Solutions for Class 11 Maths Chapter 7 Permutation and Combination from below.

Download NCERT Class 11 Maths Chapter 7 Solutions

## What will you learn in CBSE Class 11 Maths Chapter 7 Permutation and Combination?

Class 11 Maths Chapter 7 Permutations and Combinations is a part of the unit Algebra that adds up to 30 marks of the total 80 marks. The students will learn basic counting techniques & the most fundamental to the learning of these techniques in this chapter. They will learn about Factorial notation where n! represents the product of first n natural numbers i.e the product of 1 × 2 × 3 × . . . × (n – 1) × n is denoted as n!.

The Combination is based on a selection of objects & creating a group without considering their mutual ordering. There are four exercises & a miscellaneous exercise in this chapter that assist the students to understand the concepts related to Permutations and Combinations clearly.

The major concepts of Maths covered in chapter 7 solutions are:

- 1 Introduction
- 2 Fundamental Principle of Counting
- 3 Permutations
- 3.1 Permutations when all the objects are distinct
- 3.2 Factorial notation
- 3.3 Derivation of the formula for
^{n}P_{r} - 3.4 Permutations when all the objects are not distinct objects
- 4 Combinations

#### Excercise wise questions:

- Class 11 Maths chapter 7 exercise 7.1 solutions – 6 Questions
- Class 11 Maths chapter 7 exercise 7. 2 solutions – 5 Questions
- Exercise 7.3 solutions for class 11 Maths Chapter 7 9 Questions
- Class 11 Maths chapter 7 exercise 7.4 solutions – 10 questions
- Class 11 Maths chapter 7 miscellaneous exercise solutions – 11 questions

### Theorems and formulaes used in chapter

Permutation formula = **P _{r} = n!/(n-r)! ; 0 ≤ r ≤ n**

**Combination formula = _{n}C_{r} = n(n-1)(n-2)…(n-r+1)/ r! = n!/ r!(n-r)!= _{n}P_{r} /r!**

n! = 1 × 2 × 3 × …×n

n! = n × (n – 1) !

Theorems

**Theorem 1: **

When the number of permutations of n different objects are taken r at a time, the condition is 0 < r ≤ n and the objects that do not repeat = n ( n – 1) ( n – 2)……( n – r + 1). So, the notation that denote the permutation is ^{n }P_{r}

**Theorem 2: **

The number of permutations of different objects n are taken r at a time & if repetition is allowed, it is n^{r} .

**Theorem 3**:

If want to find the number of permutations of the objects n and p are the objects of the same kind and remaining are all different, it is n! / p!

**Theorem 4**:

The number of permutations of n objects if p_{1} are the objects of one kind & p_{2} are the objects of the second kind.

p_{k }is of the k^{th} kind and the remaining are of a different kind then the permutation is n! / (p_{1}!p_{2}!…P_{k}!)

**Theorem 5**:

If 0 < r ≤ n.

^{n}P_{r } = ^{n}C_{r }r!

**Theorem 6:**

** ^{n}**C

_{r }+

^{n}C

_{r-1}=

^{n+1}C

_{r}

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