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Revision Notes

Permutations and Combinations

Kerala Board · Class 12 · Mathematics

Quick revision notes for Permutations and Combinations — Kerala Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions20 flashcards5 concepts

Key Topics to Revise

1

1. Fundamental Principle of Counting

  • If an event can occur in m ways and after it occurs, another event can occur in n ways, then both events together can occur in m × n ways
  • This principle extends to multiple events: m₁ × m₂ × m₃ × ... × mₙ ways
  • Used as the foundation for all permutation and combination calculations
2

2. Factorial Notation and Basic Properties

  • n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
  • 0! = 1 by definition (very important to remember)
  • n! = n × (n-1)! for n ≥ 1
3

3. Permutations (Arrangements)

  • Permutation is an arrangement where order matters
  • Total permutations of n objects = n!
  • Permutations of r objects from n objects = ⁿPᵣ = n!/(n-r)!
4

4. Permutations with Restrictions

  • Objects together: Treat grouped objects as one unit
  • Objects not together: Use total arrangements minus arrangements where they are together
  • Fixed positions: Place restricted objects first, then arrange others

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Full Notes

Key Concepts

If event A can occurn! = n × (nNumber of ways to arrange rNumber of ways to select rArrangements in a circle where rotations

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Frequently Asked Questions

What are the important topics in Permutations and Combinations for Kerala Board Class 12 Mathematics?

Permutations and Combinations covers several key topics that are frequently asked in Kerala Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.

Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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 31 chapters — Kerala Board Class 12 Mathematics Revision Notes