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Permutations and Combinations — Revision Notes

CBSE · Class 11 · Applied Mathematics

Permutations and Combinations revision notes for CBSE Class 11 Applied Mathematics: 4 topics in quick points. Includes Factorial and Basic Counting.

45 questions24 flashcards2 formulas & key relations5 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?
Key topics in Permutations and Combinations include Factorial and Basic Counting Principles, Permutations, Combinations, Applications and Problem Solving. Study these first, then practise questions on each for Class 11 exams.
How should I revise Permutations and Combinations for Class 11 exams?
Learn the core ideas first, then work through the 45 practice questions on Permutations and Combinations. Revise 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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All CBSE Class 11 Applied Mathematics Revision Notes

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