NCERT Class 11 Mathematics Mathematics: Chapter 6 — MATHEMATICS
This chapter introduces the fundamental concepts of Permutations and Combinations in Mathematics for Class 11 CBSE students. It begins with an engaging introduction using a number lock problem to highlight the need for efficient counting techniques. The chapter then explains the Fundamental Principle of Counting with practical examples, such as Mohan choosing pants and shirts, and Sabnam selecting school bags, tiffin boxes, and water bottles. These examples illustrate how to calculate the total number of possible arrangements by multiplying the number of choices for each item. This principle forms the basis for understanding more complex counting methods in subsequent sections, aiding students in solving problems without exhaustive listing.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 6 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 480 |
Learning outcomes
- Understand the need for basic counting techniques.
- Learn and apply the Fundamental Principle of Counting.
- Solve problems involving multiple choices and arrangements.
- Recognize the application of counting principles in real-life scenarios.
Vocabulary
| Word | Meaning |
|---|---|
| Permutations | Arrangements of objects in a specific order. |
| Combinations | Selections of objects where order does not matter. |
| Fundamental Principle of Counting | A rule for determining the total number of ways an event can occur. |
| Sequence | A particular order in which related events, movements, or things follow each other. |
| Arrangement | The action, process, or result of arranging or being arranged. |
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Practice questions
- If there are 3 choices for a shirt and 4 choices for a pant, how many different pairs of shirt and pant can be chosen? Answer: 12
- A meal consists of one starter, one main course, and one dessert. If there are 2 starters, 3 main courses, and 2 desserts, how many different meals can be chosen? Answer: 12
Practice MCQs
Q1. How many ways can Mohan dress up if he has 3 pants and 2 shirts?
Explanation: According to the Fundamental Principle of Counting, the total number of ways is the product of the number of choices for each item: 3 pants × 2 shirts = 6 ways.
Q2. Sabnam has 2 school bags, 3 tiffin boxes, and 2 water bottles. How many ways can she carry one of each?
Explanation: Using the Fundamental Principle of Counting, multiply the number of choices for each item: 2 bags × 3 tiffin boxes × 2 water bottles = 12 ways.
Q3. The Fundamental Principle of Counting is also known as:
Explanation: The Fundamental Principle of Counting, when used for sequential events, is essentially the Multiplication Principle.
Frequently asked questions
What is the main purpose of the Fundamental Principle of Counting?
The Fundamental Principle of Counting helps determine the total number of ways an event can occur by multiplying the number of choices for each step, without needing to list all possibilities.
How does the number lock example illustrate the need for counting techniques?
The number lock example shows that manually checking all possible sequences for a lock can be very time-consuming, highlighting the need for efficient counting methods.
What is the difference between permutations and combinations?
Permutations are about arrangements where the order matters, while combinations are about selections where the order does not matter. This chapter focuses on the counting principles.
Can the Fundamental Principle of Counting be used for more than two events?
Yes, the principle can be extended to any number of sequential events. You multiply the number of choices for each event to find the total number of ways.
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NCERT Class 11 Mathematics — Mathematics — Chapter 6 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.