Permutation and Combination
Permutation and Combination are important topics in quantitative aptitude that deal with counting arrangements and selections. These concepts are widely used in probability and logical reasoning.
Fundamental Principles
Permutation
Arrangement of objects where order matters.
Combination
Selection of objects where order does not matter.
Factorial
n! = n × (n−1) × (n−2) × ... × 1.
Essential Formulation Tips
- Check whether order matters (Permutation vs Combination).
- Memorize factorial values up to 10.
- Simplify factorials before calculating.
- Use logic instead of brute force counting.
Shortcut Execution Techniques
- nPr = n! / (n−r)!
- nCr = n! / [r!(n−r)!]
- nCr = nC(n−r)
- Circular permutation = (n−1)!
Contextual Inquiries (FAQs)
Q: What is the difference between permutation and combination?
A:
Q: How to solve quickly in exams?
A:
Example Breakdown: Permutation Example
Basic permutation.Use formula: nPr = n!/(n−r)!
5P3 = 5! / 2! = (5×4×3×2×1)/(2×1) = 60.
Final Answer: 60.
Example Breakdown: Combination Example
Basic combination.Use formula: nCr = n!/[r!(n−r)!]
5C2 = 5!/(2!×3!) = (5×4)/2 = 10.
Final Answer: 10.
Example Breakdown: Word Arrangement Example
Common exam question.Total letters = 3.
Arrangements = 3! = 6.
Final Answer: 6.
Permutation & Combination Practice Questions
Solve important P&C questions for banking, SSC, CMAT, and placement exams.
Q1. Find 6P2.
Q2. Find 5C3.
Q3. How many arrangements of 4 letters?