NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.3 Permutations and Combinations - PDF Download

NCERT solutions for class 11 maths chapter 6 exercise 6.3 permutation and combination explains how the formula nPr is derived and how it can be used to solve problems by finding the permutation. In this part, you will be able to look at various situations where you can use different permutations on different objects. Additionally, you will also learn various theorems which are the result of the permutation formula. 

Class 11 maths chapter 6 exercise 6.3 NCERT solutions contains numerous examples to demonstrate the utilization of these formulas for the calculation of permutations. Ex 6.3 class 11 maths chapter 6 provides a variety of questions that covers the topic completely and effectively. In this exercise, there are 11 questions that are enough to give you the conceptual knowledge in a simple way.

Ex 6.3 class 11 maths solutions are designed by the academic team of mathematics at eSaral which are elaborated in simple language to help you score good marks in exams. These solutions are also available in downloadable PDF format. You can easily download the PDF for free from the official website of eSaral.   

Topics Covered in Exercise 6.3 Class 11 Mathematics Questions 

Ex 6.3 class 11 maths ch 6 permutations and combinations discusses some significant topics which includes Derivation of the formula for nPr , Permutations when all the objects are not distinct objects and some important theorems associated with permutations. Here, our subject experts of eSaral have explained these topics precisely which you can check below.

1. Derivation of the formula for

In this section, you will get to learn how to derive the formula of permutation.

Formula of permutation is given by -  ⁿP_r = $\frac{n !}{(n-r) !}$ , where 0 ≤ r ≤ n  

Theorem 2: The number of permutations of n different objects taken r at a time, where repetition is allowed, is n^r.

2. Permutations when all the objects are not distinct objects

This section has two theorems which you must learn before solving exercise questions. The two main theorems are:

Theorem 3: The number of permutations of n objects, where p objects are of the same kind and rest are all different = $\frac{n !}{p !}$ .

Theorem 4: The number of permutations of n objects, where p1 objects are of one kind, p2 are of second kind, ..., pk are of k th kind and the rest, if any, are of different kind is $\frac{n !}{p_{1} ! p_{2} ! \ldots p_{k} !}$

Tips for Solving Exercise 6.3 Class 11 Chapter 6 Permutations and Combinations

NCERT solutions for class 11 maths chapter 6 ex 6.3 is an excellent resource that gives you the in-depth understanding of each permutation concept and the formulas used for it. eSaral’s expert teachers have provided some useful tips and tricks to solve ex 6.3 class 11 chapter 6.

1. In order to solve the questions in this exercise, students need to overcome any doubts they may have about the fundamental concepts and patterns of Permutations.

2. It is recommended that class 11 students revise chapter 6 ex 6.3 of NCERT solutions class 11 maths at least twice in order to reinforce fundamental concepts and to familiarize themselves with the formulas.

3. Students must understand the theorems given in this chapter to solve questions without any confusion. 

Importance of Solving Ex 6.3 Class 11 Maths Chapter 6 Permutations and Combinations

The solutions provided for the questions in NCERT solutions class 11 maths chapter 6 ex 6.3 are easy to understand. You will get many advantages of solving ex 6.3 class 11 maths.

1. NCERT solutions for class 11 maths chapter 6 ex 6.3 has explained the derivation of formula permutation which is essential to comprehend before solving ex 6.3 questions.

2. These solutions also include some important theorems associated with permutations which builds a strong foundation for solving exercise questions. 

3. These solutions will provide students with clear and well-structured questions that will help them to understand all complex concepts step by step.

4. NCERT solutions PDF will allow you to cross check your answers of all the questions.
   

Frequently Asked Questions

Question 1. Where can I get the complete solutions for ex 6.3 class 11 maths chapter 6?

Answer 1. You can find all the solutions related to ex 6.3 class 11 maths on the eSaral website. eSaral provides step by step solutions for each question asked in ex 6.3. These solutions will help you to prepare for your exams.

Question 2. How many theorems are described in ex 6.3 class 11 maths chapter 6 permutations and combinations?

Answer 2. There are three theorems included in ex 6.3 which provide significant concepts related to permutation. These theorems are:

1. Theorem: The number of permutations of n different objects taken r at a time, where repetition is allowed, is n^r.

2. Theorem: The number of permutations of n objects, where p objects are of the same kind and rest are all different = $\frac{n !}{p !}$ .

3. Theorem: The number of permutations of n objects, where p₁ objects are of one kind, p₂ are of second kind, ..., p_k are of k th kind and the rest, if any, are of different kind is $\frac{n !}{p_{1} ! p_{2} ! \ldots p_{k} !}$