NCERT solutions for Class 11 Mathematics Chapter 6 Permutations and Combinations – complete answers & explanations

Permutations and Combinations is an important chapter in Class 11 Mathematics that helps students understand how to count and arrange objects in different ways. This chapter builds a strong foundation for topics like probability and higher-level mathematics. Students learn how to calculate arrangements, selections, and different possible outcomes using logical methods. It is especially useful in exams as many questions are directly based on formulas and concepts from this chapter. These clear and reliable NCERT solutions help students check their answers and understand the correct approach to solving problems. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance and strengthen your understanding step by step.

What this NCERT chapter covers?

1. The concept of permutations, which explains how objects can be arranged in different orders.
2. The concept of combinations, which focuses on selecting items without considering order.
3. Understanding factorial notation and its use in calculations.
4. Difference between permutations and combinations with practical examples.
5. Application of formulas in solving real-life arrangement problems.
6. Step-by-step problem-solving methods to improve logical thinking.
7. Various types of counting techniques used in mathematics.
8. Practice of numerical problems that are important for exams.
9. Development of analytical skills required for competitive exams.
10. Understanding how to apply formulas correctly in different situations.

How to use these NCERT solutions?

1. Start by attempting each question from the worksheet on your own before checking the answers.
2. Compare your answers carefully with the solutions provided here.
3. Identify mistakes and understand where your approach needs improvement.
4. Follow the exact order of questions to stay aligned with your worksheet.
5. Practice similar types of problems to strengthen your concepts.
6. Parents and teachers can guide students by discussing incorrect answers.
7. Revise formulas regularly while using these solutions.
8. Focus on accuracy and step-by-step solving rather than memorizing answers.

Important tips & tricks for students

1. Always understand whether the question requires permutation or combination before solving.
2. Learn and revise factorial values to save time during exams.
3. Avoid common mistakes like confusing order and selection.
4. Practice regularly to improve speed and accuracy.
5. Carefully read each question to understand what is being asked.
6. Double-check calculations to avoid small errors.
7. Write answers clearly and neatly for better presentation.
8. Practice a variety of questions to gain confidence.
9. Use formulas correctly and avoid skipping steps.

NCERT solutions – complete answer key

EXERCISE 6.1

1 (i) 125 
(ii) 60 

2 90 

3 (i) 5040 

4 336 

5 8 

6 20 

EXERCISE 6.2

1 (i) 40320 
(ii) 18 

2 No 

3 28 

4 336 

5 (i) 30 
(ii) 15120 

EXERCISE 6.3

1 504 

2 4536 

3 60 

4 120 
48 

5 56 

6 8 

7 (i) 3 
(ii) 5 

8 40320 

9 (i) 360 
(ii) 720 
(iii) 240 

10 3113510400 

11 (i) 360 
(ii) 720 
(iii) 240 

EXERCISE 6.4

1 45 

2 (i) 6 
(ii) 5 

3 210 

4 40 

5 200 

6 17160 

7 2380 

8 200 

9 21 

Why NCERT solutions help students?

NCERT solutions play an important role in helping students prepare effectively for exams by providing clear and accurate answers. They improve concept clarity, help students understand the correct method of solving questions, and build confidence through regular practice. With consistent use, students can strengthen their problem-solving skills and perform better in assessments.

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