NCERT Solutions for Exercise 7.2 Class 11 Maths Chapter 7 - Permutations and Combinations

# NCERT Solutions for Exercise 7.2 Class 11 Maths Chapter 7 - Permutations and Combinations

Edited By Ravindra Pindel | Updated on Jul 12, 2022 06:45 PM IST

In the previous exercise, you have already learned about the fundamental principle of counting. In this article, you will get NCERT solutions for Class 11 Maths Chapter 7 exercise 7.2 where you will learn about the counting technique called "Permutations". It is a very important concept based on the fundamental principle of counting. Also, you will get questions from topics such as permutations when all the objects are distinct and factorial notation in the Class 11 Maths chapter 7 exercise 7.2 solutions. You should try to solve all the problems given in the Class 11 Maths chapter 7 exercise 7.2. You can take help from Class 11 Maths chapter 7 exercise 7.2 solutions if you are finding difficulty while these NCERT problems.

NCERT solutions for Class 11 Maths Chapter 7 exercise 7.2 are not only important to understand the permutations but are very useful in the chapter like probability also. Also, check NCERT solutions if you are looking for the NCERT solutions from Classes 6 to 12 for Science and Maths at one place.

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## Question:1(i) Evaluate $\; 8 !$

Factorial can be given as :

$8!=8\times 7\times 6\times 5\times \times 4\times 3\times 2\times 1=40320$

Question:1(ii) Evaluate $\; 4!-3!$

Factorial can be given as :

$(ii)\; 4!-3!$

$=( 4\times 3\times 2\times 1)-(3\times 2\times 1)$

$=24-6$

$=18$

Factorial can be given as :

To prove : $3!+4!=7!$

R.H.S : $3!+4!$

$=(3\times 2\times 1)+( 4\times 3\times 2\times 1)$

$=6+24$

$=30$

L.H.S : $7!$

$=7\times 6\times 5\times 4\times 3\times 2\times 1=5040$

$L.H.S\neq R.H.S$

To compute the factorial :

$\frac{8!}{6!\times 2!}=\frac{8\times 7\times 6!}{6!\times 2\times 1}$

$=\frac{8\times 7}{ 2}$

$=4\times 7=28$

Factorial can be given as :

To find x : $\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!},$

$R.H.S :\, \, \frac{1}{6!}+\frac{1}{7!}$

$= \frac{1}{6!}+\frac{1}{7\times 6!}$

$= \frac{1}{6!}(1+\frac{1}{7})$

$= \frac{1}{6!}(\frac{8}{7})$

$L.H.S:\, \, \frac{x}{8!},$

$=\frac{x}{8\times 7\times 6!}$

Given : $L.H.S= R.H.S$

$\frac{1}{6!}\left ( \frac{8}{7} \right )=\frac{x}{8\times 7\times 6!}$

$\Rightarrow \, \, 8=\frac{x}{8}$

$\Rightarrow \, \, x=8\times 8=64$

$\; n=6,r=2$

To evaluate $\frac{n!}{(n-r)!},$

Put $n=6,r=2$

$\frac{n!}{(n-r)!}=\frac{6!}{(6-2)!}$

$=\frac{6!}{4!}$

$=\frac{6\times 5\times 4!}{4!}$

$=6\times 5=30$

$\; n=9,r=5$

To evaluate $\frac{n!}{(n-r)!},$

Put $n=9,r=5$

$\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}$

$=\frac{9!}{4!}$

$=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!}$

$=9\times 8\times 7\times 6\times 5=15120$

## More About NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.2:-

Class 11 Maths chapter 7 exercise 7.2 consists of questions related to finding the permutations when all the objects are distinct, factorial notation, and finding the value of factorials, etc. There are some theorems and examples given before the exercise 7.2 Class 11 Maths. You can go through these examples and theorems to understand the concept clearly. All the problems in the Class 11 Maths chapter 7 exercise 7.2 are very basic which you can solve very easily but the concept of this exercise will be useful in the upcoming exercises of this chapter.

## Benefits of NCERT Solutions for Class 11 Maths Chapter 7 Exercise 7.2:-

• Class 11 Maths chapter 7 exercise 7.2 solutions are designed in a descriptive manner which could be understood by an average student also.
• Class 11 Maths chapter 7 exercise 7.2 solutions are created based on the CBSE guideline, so you rely upon these solutions
• Class 11 Maths chapter 7 execise 7.2 are useful for the quick revision before the CBSE exam also.

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## Subject Wise NCERT Exampler Solutions

Happy learning!!!

1. Evaluate 3!

3! = 1x2x3 = 6

2. Evaluate 6 ! – 4!

6! -4! = 1x2x3x4x5x6 - 1x2x3x4 = 720 - 24 = 696

3. Is 2 ! + 4 ! = 6 ! ?

2 ! + 4 ! = 1x2 + 1x2x3x4 =  2 + 24 = 26

6! = 1x2x3x4x5x6 = 720

Hence 2 ! + 4 ! is not equal to 6 !.

4. What is the wieghtage of algebra in the CBSE Class 11 Maths ?

Algebra has 30 marks weightage which is the highest in the CBSE Class 11 Maths final exam.

5. What is the wieghtage of permutations & combinations in the JEE Main exam ?

Permutations & Combinations has 3.3 % weightage in the maths JEE Main.

6. What is the wieghtage of sequences & series in the JEE Main exam ?

Sequences & Series has 6.6 % weightage in the maths JEE Main.

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