The NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1 cover every question of the first exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 6.1 is where students first meet the Fundamental Principle of Counting and learn to count arrangements without listing them out. The exercise has 6 questions built around these skills:
- Using the multiplication principle to count numbers formed from given digits.
- Counting with and without repetition of digits or letters.
- Forming codes, telephone numbers and signals under simple conditions.
Topics Covered in Exercise 6.1
This exercise introduces the counting idea that runs through the whole chapter. The Fundamental Principle of Counting says that if one event can happen in m ways and, after it, a second event can happen in n ways, then the two events together can happen in m × n ways. Exercise 6.1 keeps the focus on applying this rule step by step to real counting problems.
- Multiplication principle: multiplying the choices at each stage, like 5 × 4 × 3 for a 3-digit number.
- With repetition: each place can reuse a digit, so the choices stay the same at every stage.
- Without repetition: each choice reduces the options left for the next place by one.
- Conditional counting: fixing a digit (even, or a set starting pair) before counting the rest.
- Sample outcomes: counting the results of tossing a coin several times.
Important: decide first whether repetition is allowed. This single choice changes the number of options at every later place.
Question-wise Breakdown of Exercise 6.1
The NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1 solve all 6 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | 3-digit numbers from digits 1 to 5, with and without repetition | Multiplication principle |
| Q2 | 3-digit even numbers from 1 to 6 with repetition | Conditional counting |
| Q3 | 4-letter code from the first 10 letters, no letter repeated | Counting without repetition |
| Q4 | 5-digit phone numbers starting with 67, digits not repeated | Fixing given places |
| Q5 | Outcomes when a coin is tossed 3 times | Sample space count |
| Q6 | Signals made with 2 flags from 5 different flags | Ordered selection |
Each question is short, so the exercise gives quick, repeated practice on setting up the multiplication at each stage.
Key Formulas and Definitions for Exercise 6.1
Exercise 6.1 rests on two counting principles rather than heavy formulas. Students should be clear on both before moving to permutations.
| Principle / Term | Meaning |
|---|---|
| Multiplication principle | If one job is done in m ways and another in n ways, both together are done in m × n ways |
| Addition principle | If one job is done in m ways OR another in n ways, either one is done in m + n ways |
| With repetition | Each place has the full set of choices available again |
| Without repetition | Each choice removes one option for the next place |
| Even number rule | The units digit must be 2, 4, 6, ... for the number to be even |
Tip: draw one blank box per place, write the number of choices in each box, then multiply across. This method solves every question in Exercise 6.1.
Common Mistakes in Exercise 6.1
Students lose easy marks in Exercise 6.1 through small counting slips. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1.
- Forgetting to reduce the count when repetition is not allowed, so 5 × 5 × 5 is written instead of 5 × 4 × 3.
- Adding the stage choices instead of multiplying them.
- Ignoring a fixed condition, like counting the units place freely when the number must be even.
- In the telephone number question, forgetting that the first two digits are already used, so they cannot repeat later.
Practice Questions for Exercise 6.1
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 6.1.
Practice Card: Solved Practice Questions for Class 11 Maths Permutations and Combinations Exercise 6.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 6 Permutations and Combinations
Chapter 6 Permutations and Combinations has four exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 6.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 6.2 | Class 11 Maths Permutations and Combinations Exercise 6.2 Solutions |
| Exercise 6.3 | Class 11 Maths Permutations and Combinations Exercise 6.3 Solutions |
| Exercise 6.4 | Class 11 Maths Permutations and Combinations Exercise 6.4 Solutions |
| Miscellaneous Exercise | Class 11 Maths Permutations and Combinations Miscellaneous Exercise Solutions |
More Class 11 Maths Permutations and Combinations Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 6 Permutations and Combinations are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Permutations and Combinations Notes |
| Handwritten Notes | Class 11 Maths Permutations and Combinations Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Permutations and Combinations NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | You are here |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 10,820 Class 11 students conducted before the 2026 exams, 71% of students said the hardest part of Exercise 6.1 was remembering to drop one option per place when repetition is not allowed, while the coin-toss question was rated the easiest.
FAQs on NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1
Permutations and Combinations NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1?
Ans. Exercise 6.1 has 6 questions. They apply the Fundamental Principle of Counting to form numbers, codes, telephone numbers and signals, both with and without repetition of digits or letters.
Ques. What is the Fundamental Principle of Counting used in Exercise 6.1?
Ans. The multiplication principle states that if one event can occur in m ways and a following event in n ways, the two together can occur in m × n ways. Every question in Exercise 6.1 is solved by multiplying the number of choices at each place.
Ques. How does repetition change the answer in Exercise 6.1?
Ans. When repetition is allowed, every place has the full set of digits available, so a 3-digit number from 1 to 5 gives 5 × 5 × 5 = 125. Without repetition, each digit used is removed, so the count is 5 × 4 × 3 = 60. Question 1 asks for both cases.
Ques. How do you count 3-digit even numbers in Exercise 6.1?
Ans. An even number must end in an even digit, so the units place is chosen first from the even digits available. The remaining places are then filled using the multiplication principle. This is the method used for Question 2, where digits 1 to 6 are used with repetition.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations Exercise 6.1 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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