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.
Example Breakdown: Permutation Basic
Basic permutation conceptUse permutation: n! = 3!
3! = 3 × 2 × 1 = 6
Example Breakdown: Combination Basic
Basic combination problemnCr = 4C2
= 4! / (2! × 2!)
= 6
Example Breakdown: Permutation Formula
CMAT standard question5P2 = 5! / 3!
= (5 × 4 × 3!) / 3!
= 20
Example Breakdown: Combination Formula
Frequently asked CMAT question6C3 = 6! / (3! × 3!)
= 20
CMAT Permutation Basics Set 1
Fundamental arrangement and factorial-based permutation questions.
Q1. How many ways can 4 students be arranged in a row?
Q2. Find 5P2.
Q3. In how many ways can 3 books be arranged on a shelf?
Q4. How many ways can 5 people sit in a line?
Q5. Find 4P3.