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Permutations and Combinations — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Permutations and Combinations revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

57 questions30 flashcards9 formulas & key relations5 concepts

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Key Topics to Revise

1

Fundamental Principle of Counting

  • If one event can occur in 'm' ways and a second event can occur in 'n' ways after the first, then both events together can occur in m × n ways.
  • This principle can be extended to more than two events.
  • Used to find total number of outcomes without listing them all.
2

Factorial Notation and Permutations

  • Factorial of a number n is the product of all positive integers from 1 to n.
  • Permutation means arrangement of objects where order matters.
  • Number of permutations of n different objects taken all at a time is n!.
3

Combinations

  • Combination means selection of objects where order does not matter.
  • Number of combinations of r objects out of n is denoted by nCr.
  • Each combination corresponds to multiple permutations.
4

Special Cases and Applications

  • Circular permutations: Arranging objects in a circle where rotations are considered same.
  • When clockwise and anticlockwise arrangements are identical (like garlands), divide by 2.
  • Permutations with restrictions: Handle special conditions first.

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Full Notes

Key Concepts

If one event can occurFor a positive integer nA permutation is an arrangementA combination is a selectionWhen arranging n distinct objects

Frequently Asked Questions

What are the important topics in Permutations and Combinations for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Permutations and Combinations include Fundamental Principle of Counting, Factorial Notation and Permutations, Combinations, Special Cases and Applications. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Permutations and Combinations for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 57 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 Telangana Open School (TOSS) Class 12 Mathematics Revision Notes

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