NCERT Solutions Class 11 Mathematics Chapter 7- Permutations and Combinations
Mathematics can be a complex subject in which students tend to find many concepts difficult to comprehend. Hence, it is essential for students to understand the crux of the problem to solve it correctly. The NCERT Solutions Class 11 Mathematics Chapter 7 is a reliable and convenient learning resource. It will help to perform strategic learning and enable regular practice.
Through explicit answers to the textual problems NCERT Solutions Class 11 Mathematics Chapter 7 explains all fundamental concepts based on Permutations and Combinations. Its basic applications involve arranging numbers, alphabets, etc., in a specific order. They also have various applications in the fields of computer science and physics.
Having a deep knowledge of Class 11 Mathematics Chapter 7 is crucial. With the help of NCERT Solutions Class 11 Mathematics Chapter 7, students will build their core fundamentals and get well-versed with this topic.
Students are encouraged to refer to NCERT Solutions Class 10, NCERT Solutions Class 9 and NCERT Solutions Class 8 which will help them score better in their examinations.
Key Topics Covered in NCERT Solutions Class 11 Mathematics Chapter 7
The Chapter 7 Mathematics Class 11 is very important for each student to attain high scores in the examinations. With the help of NCERT Solutions Class 11 Mathematics Chapter 7 provided by the Extramarks, students can attain the required knowledge and solve unlimited questions and exercises provided in these solutions.
To master the Class 11 Mathematics NCERT solutions Chapter 7, students will have to study the following topics thoroughly:
| Exercise |
Topic |
| 7.1 |
Introduction |
| 7.2 |
Fundamental Principle of Counting |
| 7.3 |
Permutations |
| 7.4 |
Combinations |
7.1 Introduction:
In the NCERT Solutions Class 11 Mathematics Chapter 7, students will learn about Permutations and Combinations. The topics included in the solutions are factorial notation, principles of counting permutations, derivation of formulas and theorems. In the Class 11 Mathematics Chapter 7, students will learn basic techniques and different ways to arrange and select objects.
Students are advised to study using the NCERT Solutions Class 11 Mathematics Chapter 7 to avail accurate answers to the textbook exercises of this chapter.
7.2 Fundamental Principle of Counting:
This principle states that “For two events if an event occurs in ‘m’ ways. Another event occurs in ‘n’ ways, then the total number of occurrences of the events in the given order is m × n.”
For instance; If a person has 3 pants and 2 shirts. Then, the possible number of pairs that person can choose from will be 3×2= 6
For 3 events, the principle is as follows: “If an event occurs in m ways, and another event occurs in n ways, after which a third event occurs in p ways, then a total number of occurrences in the given order will be m × n × p.”
There are two types of questions that are included in the NCERT Solutions Class 11 Mathematics Chapter 7.
- The number of ways the following events occur in succession:
(i) Choosing a pant
(ii) Choosing a shirt
- The required number of ways is the number of ways an event occurs in succession:
(i) Choosing a school bag
(ii) Choosing a tiffin box
(iii) Choosing a water bottle.
In both the above cases, the events may occur in various orders. But, we must choose any one order and count the number of different ways the event occurs.
7.3 Permutations:
In this section of NCERT Solutions Class 11 Mathematics Chapter 7, students will learn about permutations. It is defined as the arrangement in a definite order of a number of objects chosen some or all at a single time.
Theorem 1: When objects are distinct, say n, the number of permutations taken r at a time, as 0 < r ≤ n then the objects do not repeat. It is n ( n – 1) ( n – 2). . .( n – r + 1) and is denoted by Prn.
Factorial notation:
Under this section of permutation, students will learn to denote the product of several numbers such as 1 x 2 x 3 x 4 x 5 x …. X (n-1) x n = n!
The formula for Permutation, Prn = n!(n-r)! , where 0 < r ≤ n is very important. Students will also learn the derivation of this formula. Theorem 1 which states that the number of permutations of distinct objects, say n, taken r at a time with repetition is given as nr.
When the number of objects are not distinct, p objects are the same kind, and the rest are different is given as n!p!.
7.4 Combinations:
In this section, students will learn the way to select items from the collection in any order. Several concepts related to this topic are explained here. In the NCERT Solutions Class 11 Mathematics Chapter 7, students will learn several new formulas to solve the problems easily. The formulas are mentioned below:
- Prn = Crn r!, where 0 < r ≤ n
- Crn = n!r! (n-r)!
- Cnn = 1, where r = n
- C0n = 1
- Cn-rn = Crn = n!r! (n-r)!
- C1n = Cbn, then a = b and n = a + b
- Crn + Cr+1n = Crn+1
There are several solved examples that students must study in order to get an in-depth understanding of the NCERT Solutions Class 11 Mathematics Chapter 7 Permutations and Combinations.
NCERT Solutions Class 11 Mathematics Chapter 7: Exercise & Solutions
Students can study with the help of the NCERT Solutions Class 11 Mathematics Chapter 7 from the extramarks platform. These solutions are prepared by experts and professionals in the field of Mathematics. It comprehensively explains each and every answer of the textual exercises along with several other sums for practice. Students can depend on the Class 11 Mathematics NCERT Solutions Chapter 7 for last minute revision. It includes all important formulas, theorems, derivations and key points.
The NCERT Solutions Class 1, NCERT Solutions Class 2 and NCERT Solutions Class 3 provides a helping hand for the primary section students in the studies.
Visit the links mentioned below to get access to the Extramarks NCERT Solutions Class 11 Mathematics Chapter 7:
Extramarks also provides study materials such as CBSE sample papers, mock tests, and revision notes along with several past years’ question papers. Students are advised to refer to the best NCERT reference books and NCERT Solutions Class 12 provided by the platform of Extramarks to get a deeper understanding of all concepts. Refer to the Class 11 Mathematics Chapter 7 for efficient preparation.
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NCERT Exemplar Class 11 Mathematics
The NCERT Exemplar notes are important for annual examinations and competitive exam preparations. Students must refer to these notes to understand all complicated topics easily. The NCERT Exemplar and the NCERT Solutions Class 11 Mathematics Chapter 7 will help students to enhance their thinking abilities and problem-solving skills. It provides unlimited aptitude-based, higher levels and several twisted questions for students to practise. Students are advised to use the NCERT Exemplars provided on the Extramarks’ website to ace their examinations.
The platform of Extramarks aims to make learning better and easier through high-quality and dependable study notes. The NCERT Solutions Class 11 Mathematics Chapter 7 are prepared by subject matter enthusiasts through thorough research and analysis. The team also provides guidance and support in the student’s journey to pursue their dream careers.
Key Features of NCERT Solutions Class 11 Mathematics Chapter 7
- All concepts in the NCERT Solutions Class 11 Mathematics Chapter 7 are explained in a detailed and well-structured manner for students to understand easily.
- Students will be able to tackle tricky questions with the help of the tricks and shortcut methods included in the notes.
- The NCERT Solutions for Class 11 Mathematics Chapter 7 provided by the Extramarks platform follows the CBSE books. It also adheres to all guidelines issued by the board.
- The solutions include all the answers to the textual questions having the concepts which student needs to study, learn and revise to gain top scores in the annual examinations.
- By practising the questions of Chapter 7 Mathematics Class 11 over and over again, students can improve their time-management skills by solving all the questions in the allotted time.
- The notes aim to clear all queries and doubts of the students.
- Students preparing for entrance examinations can also refer to these NCERT Solutions Class 11 Mathematics Chapter 7.