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id: "66f15952e361cd99fe370dae"
title: "Permutations and Combinations"
board: "CBSE"
curriculum: "CBSE"
class: "Class 11"
subject: "Mathematics"
book: "Mathematics"
chapter: "Permutations and Combinations"
chapter_slug: "permutations-and-combinations"
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last_updated: "2026-06-20"
---

# Permutations and Combinations
This chapter focuses on techniques for counting arrangements and selections of objects, which are essential for solving problems involving permutations and combinations without listing every possibility.

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## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Permutations and Combinations |
| Pages | 100-125 |

---

## Chapter Summary

### Short Summary
This chapter introduces the fundamental principle of counting and explores permutations and combinations as methods for solving counting problems in various contexts.

### Detailed Summary
The chapter begins with a practical scenario involving a number lock, which leads to the exploration of counting techniques. It establishes the fundamental principle of counting, demonstrating how to count different combinations and arrangements through illustrative examples. The chapter explicates the concept of permutations where order matters and combinations where it does not, providing examples to reinforce understanding.

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## Topic-Wise Explanation

### Introduction
This section sets the stage for understanding counting techniques by presenting a real-world problem involving a locked suitcase.

### Fundamental Principle of Counting
This topic introduces the multiplication principle, explaining how to calculate total arrangements when given multiple choices, supported by examples of clothing and items.

### Permutations
This section covers the concept of permutations, illustrating how to count distinct arrangements of items, including real-life examples like forming words from letters without repetition.

### Combinations
This topic discusses combinations, where order does not matter, with illustrations that clarify how selection occurs in various situations.

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## Character Analysis

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## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Fundamental Principle of Counting | States that if an event can occur in m ways and another in n ways, the total is $m 	imes n$. |

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## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Permutations | Arrangements of a set where the order matters. |
| Combinations | Selections of a set where the order does not matter. |

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## Important Points for Revision
* The fundamental principle of counting helps solve counting problems efficiently.
* Permutations involve arrangements where position matters, while combinations involve selections where order is irrelevant.
* Example of finding 4-letter words from given letters illustrates permutations.
* Example with flags explains permutations as signals generated from colored flags.
* Combinations can be computed using the formula for binomial coefficients where order does not matter.
* Practical applications can be observed in everyday problem scenarios.
* Understanding examples is crucial for applying counting principles correctly.
* Problems can increase in complexity with additional items and choices.

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## Vocabulary and Glossary

| Word / Phrase | Meaning |
| :--- | :--- |
| Permutation | A distinct arrangement of items.
| Combination | A selection of items without regard to order. |

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## Practice Questions

### Short Answer Questions
1. How many different pairs of pants and shirts can Mohan wear?
2. What is the total number of odd 2-digit numbers that can be formed using the digits 1, 2, 3, 4, 5?
3. How many ways can Sabnam carry her school items?
4. Given 5 different flags, how many combinations of at least 2 can be made?
5. How many 4 letter words can be formed from the letters of the word ROSE without repetition?

### Long Answer Questions
1. Explain the fundamental principle of counting and provide two examples demonstrating its application.
2. How are permutations calculated, and why is the order of arrangement important? Give an example.
3. Compare and contrast permutations and combinations with suitable examples.
4. Solve a problem involving the selection of two items from a set of five distinct items. Calculate the number of ways.
5. Discuss how variations in constraints (like repetition) change the counting outcomes in combinations and permutations.

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## Related Concepts

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## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 66f15952e361cd99fe370dae |
| Canonical URL | https://www.edzy.ai/cbse-class-11-mathematics-permutations-and-combinations |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-11-mathematics-permutations-and-combinations.md |