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Permutations and Combinations

Jammu & Kashmir Board · Class 11 · Mathematics

Complete topic list for Permutations and Combinations in Jammu & Kashmir Board Class 11 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

127 questions64 flashcards5 concepts

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4 Topics · Jammu & Kashmir Board Class 11 Mathematics

Topics in Permutations and Combinations

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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.
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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.
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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.
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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.

Key Concepts

Central concept: Counting arrangements and selections of objects

Fundamental principle of countingPermutationsCombinationsFactorial notationApplications to numbers and wordsPermutations with repeated letters or objectsCombination-based counting problemsHistorical development

Frequently Asked Questions

What are the important topics in Permutations and Combinations for Jammu & Kashmir Board Class 11 Mathematics?
Permutations and Combinations covers several key topics that are frequently asked in Jammu & Kashmir Board 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 — Jammu & Kashmir Board Class 11 Mathematics?
Understand the core concepts first, then work through the 127 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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