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Permutations and Combinations — Revision Notes

CBSE · Class 11 · Mathematics

Permutations and Combinations revision notes for CBSE Class 11 Mathematics: 4 topics in quick points. Part of the CBSE Class 11 Mathematics syllabus.

127 questions64 flashcards11 formulas & key relations5 concepts

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Key Topics to Revise

1

1. Fundamental Principle of Counting

  • If one event can happen in m ways and a second event can happen in n ways, then the two events together can happen in m × n ways.
  • The same idea extends to three events: if the first has m ways, the second has n ways, and the third has p ways, then the total is m × n × p.
  • This principle is also called the fundamental principle of counting.
2

2. Factorial Notation

  • n! is the product of the first n natural numbers.
  • 0! is defined to be 1 by convention.
  • Factorial notation makes permutation and combination formulas shorter and easier to use.
3

3. Permutations of Distinct Objects

  • A permutation is an arrangement in a definite order of objects taken some or all at a time.
  • Order matters in permutations.
  • The number of permutations of n different objects taken r at a time is nPr.
4

4. Permutations with Repetition or Repeated Objects

  • If repetition is allowed, the number of permutations is n^r.
  • If some objects are identical, divide by the factorials of repeated groups.
  • Words like ROOT, ALLAHABAD, and INSTITUTE illustrate repeated objects.

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Full Notes

Key Concepts

If an event can occurA permutation is an arrangementThe number of permutations of nn! is the product ofIf repetition is allowed

Frequently Asked Questions

What are the important topics in Permutations and Combinations for CBSE Class 11 Mathematics?
Key topics in Permutations and Combinations include Fundamental Principle of Counting, Factorial Notation, Permutations of Distinct Objects, Permutations with Repetition or Repeated Objects. 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 127 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.

More resources for Permutations and Combinations

All CBSE Class 11 Mathematics Revision Notes

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