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Permutations and Combinations

Telangana Open School (TOSS) · Class 12 · Mathematics

Quick revision notes for Permutations and Combinations — Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

57 questions30 flashcards5 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?
Permutations and Combinations covers several key topics that are frequently asked in Telangana Open School (TOSS) Class 12 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 — Telangana Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 57 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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