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CMAT Topics

Permutation and Combination

Permutation and Combination help in counting arrangements and selections. These concepts are essential in TU CMAT for solving logical counting, arrangement, and probability-based problems.

Practice MCQs for Permutation and Combination

Fundamental Principles

Permutation

Permutation refers to the arrangement of objects in a specific order. Order matters in permutation problems.

Combination

Combination refers to the selection of objects where order does not matter.

Factorial

Factorial of n (n!) is the product of all positive integers from 1 to n.

Permutation Formula

Permutation of n objects taken r at a time is nPr = n! / (n-r)!.

Combination Formula

Combination of n objects taken r at a time is nCr = n! / (r!(n-r)!).

Difference Between Permutation and Combination

Permutation is arrangement (order matters), while combination is selection (order does not matter).

Essential Formulation Tips

  • Use permutation when order matters and combination when it does not.
  • Always simplify factorial expressions before calculating.
  • Use cancellation to reduce large factorials quickly.
  • Memorize values of small factorials (5!, 6!, 7!).

Shortcut Execution Techniques

  • nPr = nCr × r!
  • nCr = nC(n-r)
  • 0! = 1 always
  • Use cancellation instead of full factorial expansion
  • Break large factorials into smaller multiplications

Contextual Inquiries (FAQs)

Q: What is the main difference between permutation and combination?

A: Permutation considers arrangement (order matters), while combination considers selection (order does not matter).

Q: Which is more important for CMAT exams?

A: Both are important, but combination-based questions appear more frequently in CMAT.

Q: What is factorial used for?

A: Factorial is used to calculate permutations and combinations in counting problems.