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Permutations and Combinations

CBSE · Class 11 · Applied Mathematics

Quick revision notes for Permutations and Combinations — CBSE Class 11 Applied Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions24 flashcards5 concepts

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Key Topics to Revise

1

Factorial and Basic Counting Principles

  • Factorial (n!) = 1 × 2 × 3 × ... × n, where 0! = 1
  • Fundamental Principle of Addition: If event E can occur in m ways and event F in n ways (mutually exclusive), total ways = m + n
  • Fundamental Principle of Multiplication: If event E can occur in m ways followed by event F in n ways, total ways = m × n
2

Permutations

  • Permutation is arrangement of objects where order matters
  • ⁿPᵣ = number of ways to arrange n distinct objects taken r at a time
  • When repetition is allowed: nʳ arrangements possible
3

Combinations

  • Combination is selection of objects where order doesn't matter
  • ⁿCᵣ = number of ways to select r objects from n distinct objects
  • Important property: ⁿCᵣ = ⁿCₙ₋ᵣ
4

Applications and Problem Solving

  • Word formation problems: consider identical letters
  • Committee selection: use combinations for selection, permutations for positions
  • Geometric problems: points, lines, triangles use combinations

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Full Notes

Key Concepts

The product of first n naturalTwo basic rulesArrangements of objects where order mattersArrangements in a circle where relativeWhen some objects are identical

Frequently Asked Questions

What are the important topics in Permutations and Combinations for CBSE Class 11 Applied Mathematics?
Permutations and Combinations covers several key topics that are frequently asked in CBSE Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Permutations and Combinations — CBSE Class 11 Applied Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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