Permutation And Combinations Class 11th Notes - Free NCERT Class 11 Maths Chapter 7 notes - Download PDF

Imagine you have money to buy 2 Harry Potter books from a set of 8, and you are thinking which two combinations of books you can buy. Or, suppose your school’s football coach asks you to pick 5 players for 5 different positions from your class, and you are confused about whom to choose and for which position. This is where the concepts of Permutations and combinations come into play. We will read about these concepts in maths chapter 6 class 11. Experienced Careers360 experts prepare permutation and combinations class 11 notes to make the learning process smooth for students.

Permutations and combinations have various real-life applications and are a very important chapter for the class 11 board exam, as well as many important competitive exams. This permutation and combinations NCERT notes will strengthen the basic concepts and can be useful as a revision tool. The latest CBSE Syllabus has been followed, and the important concepts and formulas are presented in a well-structured manner in these notes. Students can also practice NCERT Exemplar Class 11 Maths Chapter 6 Permutations and Combinations, for a better understanding of these concepts.

NCERT Class 11 Maths Chapter 6 Notes

Fundamental Principle of Counting

Fundamental principle of counting is a rule used to find the total number of outcomes possible in a given situation. The fundamental principle of counting can be classified into two types.

Multiplication Rule (AND rule)

Addition Rule (OR rule)

Multiplication Rule

If a certain work W can be completed by doing 2 tasks, first doing task A AND then doing task B. A can be done in m ways and, following that, B can be done in n ways, then the number of ways of doing the work W is (m x n) ways.

For example, let's say a person wants to travel from Noida to Gurgaon, and he has to travel via New Delhi. It is given that the person can travel from Noida to New Delhi in 3 different ways and from New Delhi to Gurgaon in 5 different ways.

So, in this case, to complete his work (reach Gurgaon) he has to do two tasks one after the other, first traveling from Noida to New Delhi (task A) AND then from New Delhi to Gurgaon (task B), as he has 3 different ways of reaching New Delhi (doing task A), and he has 5 different ways to reach Gurgaon from New Delhi (doing task B), so in that way, he has a total of 3×5 = 15 different ways to reach Gurgaon from Noida.

Addition Rule

If work W can be completed by doing task A OR task B, and A can be done in m ways and B can be done in n ways (and both cannot occur simultaneously: in this case we call tasks A and B as mutually exclusive), then work W can be done in (m + n) ways.

For example, let’s say that a person can travel from New Delhi to Noida in 3 different types of buses, and 2 different types of trains, so, he can complete the work of going from New Delhi to Noida in 3 + 2 = 5 ways (As work can be completed by going by bus (A) OR by going by train (B))

Permutation

The definition refers to several possible ways of arranging or ordering a set of numbers.

There are two types of Permutation.

1. Linear Permutation

2. Circular Permutation

Linear Permutation

This is defined as when some things are arranged linearly. Like arrangement of books, pens and many more.

The formula to compute problems goes by: ${}^n{P}_r$

Consider the following example:

The above example represents a group of five different coloured balls arranged in two different orders in a straight line. Here, the starting and ending positions of the balls are different at each order.

Circular Permutation

This is defined as when something is arranged in a circular manner. Like the arrangement of chairs at a round table or the arrangement of beads in a necklace.
$P_n=n-1$

Consider the following example:

In the figure above, the five balls are arranged in two different orders in the circular form. Both the permutations look different, but they are the same. Because every ball has the same coloured ball to its right and left.

Combination

It is defined as a selection of objects without regard to order.

Now, the formula for finding the number of combinations of n different objects taken r at a time, denoted by ${}^n{C}_r$.

${}^n{C}_r=\frac{n!}{r!(n-r)!}$

Ex: Choosing 3 pens from the set of 10.
Then,
${}^{10}{C}_3=\frac{10!}{3!(10-3)!}=120$

The relationship between Permutation and Combination is:
${}^n{C}_r=\frac{{}^n{P}_r}{r!}$

Permutations Vs Combinations

Always remember, in an arrangement, the order is always important. Whereas, in Combination, the order is not important.

Consider the following examples-
1. Selecting a team of 11 from 16 players - Selection

Drawing a batting line-up of 11 from 16 players - Arrangement
2. Selecting 3 students out of 10 students who will receive scholarships of the same value - Selection

Selecting 3 students out of 10 students who will receive scholarships of Rs. 500, Rs. 1000, and Rs. 2000 - Arrangement

Importance of NCERT Class 11 Math Chapter 6 Notes

NCERT Class 11 Maths chapter 6 notes can be an essential learning tool if students use them wisely. These notes have many importance.

• These notes will clarify the concepts of Permutations and combinations. Students will understand when the order matters and when it doesn't.
• A good number of questions come from this chapter in class 11 board exams as well as in exams like JEE Main, NDA, and CUET.
• Students can use this note for quick revision of the important concepts and formulas.
• These notes will improve students' logical thinking and analytical skills.
• Completing these notes will boost the confidence of the students and create a positive vibe, which is a necessity before an exam.

NCERT Class 11 Notes Chapter Wise

Subject Wise NCERT Exemplar Solutions

Students can check these NCERT exemplar links for further practice purposes.

• NCERT Exemplar Class 11 Solutions
• NCERT Exemplar Class 11 Maths
• NCERT Exemplar Class 11 Physics
• NCERT Exemplar Class 11 Chemistry
• NCERT Exemplar Class 11 Biology

Subject Wise NCERT Solutions

After checking the Mathematics solutions, students can also check the solutions of other subjects. These solutions are well-structured and well-explained.

• NCERT Solutions for Class 11 Mathematics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Physics
• NCERT Solutions for Class 11 Biology

NCERT Books and Syllabus

Students need to be aware of the latest CBSE syllabus. Also, an extra reference book always proved handy. Here are some links that will help students with the above two causes.