Class 11 Maths Chapter 6 Permutations and Combinations – Exercise 6.1 NCERT Solutions

Introduction

Exercise 6.1 introduces the concept of permutations. You will learn how to count arrangements of objects, apply factorial notation, and solve problems involving ordered arrangements. This exercise builds the foundation for combinatorics and probability.

Key Concepts

1. Factorial Notation:

$$n!=n\cdot (n-1)\cdot (n-2)\cdots 3\cdot 2\cdot 1$$

2. Permutation Formula: Number of permutations of $n$ objects taken $r$ at a time:

$$P(n,r)=\frac{n!}{(n-r)!}$$

3. Special Cases:

   • $P(n,n)=n!$

   • $P(n,1)=n$

NCERT Questions with Solutions (10)

Q1. Find number of permutations of 5 objects taken 3 at a time.

$$P(5,3)=\frac{5!}{(5-3)!}=\frac{120}{2}=60$$

Q2. Find number of permutations of 6 objects taken 2 at a time.

$$P(6,2)=\frac{6!}{(6-2)!}=\frac{720}{24}=30$$

Q3. Find number of permutations of 4 objects taken all at a time.

$$P(4,4)=4!=24$$

Q4. Find number of permutations of 7 objects taken 1 at a time.

$$P(7,1)=7$$

Q5. Find number of permutations of 8 objects taken 3 at a time.

$$P(8,3)=\frac{8!}{(8-3)!}=\frac{40320}{120}=336$$

Q6. Find number of permutations of 9 objects taken 2 at a time.

$$P(9,2)=\frac{9!}{(9-2)!}=\frac{362880}{5040}=72$$

Q7. Find number of permutations of 10 objects taken 4 at a time.

$$P(10,4)=\frac{10!}{(10-4)!}=\frac{3628800}{720}=5040$$

Q8. Find number of permutations of 12 objects taken 5 at a time.

$$P(12,5)=\frac{12!}{(12-5)!}=\frac{479001600}{5040}=95040$$

Q9. Find number of permutations of 11 objects taken 3 at a time.

$$P(11,3)=\frac{11!}{(11-3)!}=\frac{39916800}{40320}=990$$

Q10. Find number of permutations of 6 objects taken 6 at a time.

$$P(6,6)=6!=720$$

FAQs (10)

1. What is permutation? Ordered arrangement of objects.

2. What is factorial? Product of all positive integers up to $n$.

3. What is formula for permutation? $P(n,r)=\frac{n!}{(n-r)!}$.

4. What is $P(n,n)$? Equal to $n!$.

5. What is $P(n,1)$? Equal to $n$.

6. Is order important in permutation? Yes.

7. Is repetition allowed in permutation? Not in standard formula.

8. What is difference between permutation and combination? Permutation considers order, combination does not.

9. What is domain of factorial function? Non‑negative integers.

10. Why is this exercise important? It builds foundation for combinatorics and probability.

Conclusion

Exercise 6.1 has 10 solved questions and 10 FAQs that strengthen your understanding of permutations. This builds the foundation for combinatorics and probability in Class 11 Maths.

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New Syllabus-Class 11 Maths Chapter 6 Permutations and Combinations – Exercise 6.1 NCERT Solutions