# NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations (Ex 7.2) Exercise 7.2

The topics covered in Class 11 serve as a foundation for the students studying in Class 12. Even though Classes 10 and 12 are both significant parts of every student’s academic life, Class 11 is crucial for the academic journey. Therefore, it’s important to approach every subject in Class 11 with the utmost devotion and focus.

NCERT textbooks serve as a primary source of information for Class 11 examinations. These books cover every subject that is on the CBSE syllabus with intricate detail. The NCERT book includes exercise questions at the end of each chapter to assist students in assessing their comprehension of the subjects. From the perspective of exam preparation, these practise questions are crucial.

For all subjects, NCERT Solutions for Class 11 are available on Extramarks. All necessary NCERT Solutions are available in one place. NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, and the other exercises of the chapter are also available. When necessary, examples or illustrations are used to help illustrate the solutions in clearer language. Extramarks subject matter specialists have made sure that the solutions were created in accordance with CBSE requirements. Students can use NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, to get acquainted with the pattern followed by Extramarks in all their NCERT Solutions.

This webpage has the link to download the NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2. Extramarks also provides NCERT Solutions for all classes from Classes 1 to 12. Use the links below to go to the respective Class solutions.

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NCERT Solutions Class 11 by Extramarks

Extramarks has NCERT solutions for every topic, whether students have opted to pursue science or commerce in Class 11. It is necessary to dedicate a few hours on a regular basis to solving extra questions and sample papers to adequately prepare for the regular tests. This also proves to be beneficial for future competitive test preparation as well as for better performance in Class 11 examinations. These NCERT Solutions help master the fundamentals for Class 12. This is due to the fact that the majority of competitive exams employ the same curriculum as classes 11 and 12. NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, gives a detailed idea of the process that teachers at Extramarks follow to guide students through the examinations.

NCERT Solutions for Class 11 Mathematics, NCERT Solutions for Class 11 Physics, and NCERT Solutions for Class 11 Chemistry might be beneficial when preparing for competitive exams like JEE Main and JEE Advanced.

Class 11 is important in terms of the Class 12 board examinations and has the potential to greatly influence a student’s career. The appropriate learning strategy is crucial because it will improve their academic performance. No matter what subject they are studying, they need to concentrate on thoroughly reading and comprehending NCERT textbooks. A prevalent misconception is that the topics studied in Classes 9 and 10 are repeated in Class 11’s curriculum. This may be partially accurate, but many new ideas are also presented that need the complete attention of students. NCERT books can be used to complete the CBSE-mandated curriculum quickly because it is extremely extensive. By doing so, students can continue to the revision phase and improve their comprehension of the various ideas.

Marks distributed across Class 11

In Class 11, all subjects have a total scoring value of 100, of which 80 are from the CBSE’s written examination and 20 are from internal assessment. Every subject has an 80-mark exam, with different chapters and subjects carrying varying scoring values. The average of the grades received on midterm exams and the overall grades given for projects and practicals is used to determine the grades for internal evaluation. NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, solves all the sums as they should be done in the examination. This makes sure that students receive the maximum results of their efforts. Using NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, serves as an exercise that helps to gain more marks by increasing the efficiency of the students.

Advantages of having Extramarks NCERT Class 11

The Class 11 exams are a crucial first step in getting ready for the Class 12 board exams. It should come as no surprise that practising enough NCERT questions and practice papers will be essential for improving the grades. Referring to the Class 11 NCERT Solutions has a number of advantages, some of which are listed below:

The solutions are written in plain, simple language that is easy to comprehend. This results in students experiencing less stress when studying. For example, the NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, has all the questions solved in an easy step-by-step process for ease of use by students.

Students won’t need to look through their NCERT textbooks or class notes to complete last-minute modifications because the solutions are organized in a thorough and methodical manner. NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, has all the questions solved with important points marked clearly.

The NCERT solutions include all the critical questions and detailed explanations of each response that is significant for comprehension. NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2 on this website follows the same intricate pattern. This makes NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2 the best companion for students while preparing for any examination.

To help remember the solutions longer, these solutions are accompanied by detailed explanations and examples from real-world situations. Students can explore NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2 and other solutions for their reference.

## H2 – NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations (Ex 7.2) Exercise 7.2

Mathematics can be a daunting subject, but it is a highly scored subject when prepared with proper care. NCERT solutions for Class 11 Mathematics from Extramarks serve as a great study aid for students having trouble with any particular mathematical concept. Extramarks helps students ace the examinations with high marks by providing thorough solutions for all subjects, from Class 1 to Class 12. Subject-matter specialists with years of experience teaching under the CBSE board have specifically prepared and organized the NCERT Solutions for class 11 Mathematics. These solutions were created to assist students in gettin answers to their concerns and having a step-by-step process for resolving challenging mathematical problems. The NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2 has been solved with the same diligence by a  faculty that is equally competent and learned.

Class 11 Maths Chapter 7 Exercise 7.2, has many questions. Some questions are simple, and some require more thought. Some questions might be difficult and require external help. Not all questions can be solved by students in one go. The NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2, includes the solution for all the sums in Class 11 Maths Exercise 7.2. These solutions make a great guide for students who are solving the exercise for the first time. It is also beneficial for students who want to do a quick revision towards the end of their school year.

### H2 – NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Exercise 7.2

Permutations and combinations are ways of representing groups of objects by selecting them and subletting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation, and the order in which they are presented is called a combination.

Permutations and combinations are very crucial concepts to understand in Mathematics.

Permutations and Combinations are based on the following formulas

Permutations are: nPr = n!/(n-r)!

Combinations are: nCr = n!/[r! (n-r)!]

To understand these important concepts students must refer to the NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2. It deals with core concepts of Permutations and Combinations with Class 11 Maths Exercise 7.2. Learners can use the NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2 while practising the exercise.

The NCERT Solutions For Class 11 Maths Chapter 7 Exercise 7.2  is available on the official website of the Extramarks in downloadable PDF format. Students can download this anytime and use it as per their requirements.

Q.1 Evaluate: (i) 8! (ii) 4! – 3!

Ans.
(i) 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 40320
(ii) 4! – 3! = 4 × 3 × 2 × 1 – 3 × 2 × 1
= 24 – 6
= 18

Q.2 Is 3! + 4! = 7! ?

Ans.
3! + 4! = 3 × 2 × 1 + 4 × 3 × 2 × 1
= 6 + 24
= 30
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
= 5040
No, 3! + 4! ≠ 7!

Q.3

$\mathrm{Compute}:\frac{8!}{6!×2!}$

Ans.

$\begin{array}{l}\frac{8!}{6!\text{ }×\text{ }2!}=\frac{\text{8}×\text{7}×\text{6}×\text{5}×\text{4}×\text{3}×\text{2}×\text{1}}{\text{6}×\text{5}×\text{4}×\text{3}×\text{2}×\text{1}×\text{2}×\text{1}}\\ \text{ }=\frac{\text{8}×\text{7}}{\text{2}×\text{1}}\\ \text{ }=28\end{array}$

Q.4

$\mathrm{If}\text{\hspace{0.17em}}\frac{1}{6!}+\frac{1}{7!}=\frac{\mathrm{x}}{8!},\mathrm{find}\mathrm{x}.$

Ans.

$\begin{array}{l}\mathrm{We}\text{ are given}\\ \text{ }\frac{1}{6!}+\frac{1}{7!}=\frac{\text{x}}{8!}\\ \text{ }\frac{1}{6!}+\frac{1}{7.6!}=\frac{\text{x}}{8!}\\ \text{ }\frac{1}{6!}\left(1+\frac{1}{7}\right)=\frac{\text{x}}{8!}\\ \text{ }\frac{1}{6!}\left(\frac{7+1}{7}\right)=\frac{\text{x}}{8!}\\ \text{ }\frac{1}{6!}\left(\frac{8}{7}\right)=\frac{\text{x}}{8!}\\ \text{ }\frac{8}{7!}=\frac{\text{x}}{8.\left(7!\right)}\\ \text{ }8=\frac{\text{x}}{8}\\ ⇒\text{ x}=64\end{array}$

Q.5

$\begin{array}{l}\mathbf{Evaluate}\frac{\mathbf{n}\mathbf{!}}{\mathbf{\left(}\mathbf{n}\mathbf{–}\mathbf{r}\mathbf{\right)}\mathbf{!}}\mathbf{,}\mathbf{\text{​​}}\mathbf{when}\\ \mathbf{\left(}\mathbf{i}\mathbf{\right)}\mathbf{\text{\hspace{0.17em}}}\mathbf{n}\mathbf{=}\mathbf{6}\mathbf{,}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}}}\mathbf{r}\mathbf{=}\mathbf{2}\mathbf{}\mathbf{\left(}\mathbf{ii}\mathbf{\right)}\mathbf{}\mathbf{n}\mathbf{=}\mathbf{9}\mathbf{,}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}}}\mathbf{r}\mathbf{=}\mathbf{5}\mathbf{.}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{i}\right)\text{\hspace{0.17em}}\mathrm{n}=6,\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{r}=2\\ \frac{\mathrm{n}!}{\left(\mathrm{n}-\mathrm{r}\right)!}=\frac{6!}{\left(6-2\right)!}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \hspace{0.17em}}=\frac{6×5×4!}{4!}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}}=30\\ \left(\mathrm{ii}\right)\mathrm{n}=9,\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{r}=5\\ \frac{\mathrm{n}!}{\left(\mathrm{n}-\mathrm{r}\right)!}=\frac{9!}{\left(9-5\right)!}\\ \begin{array}{l}\text{\hspace{0.17em} \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{9×8×7×6×5×4!}{4!}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=15120\end{array}\end{array}$