Permutation & Combination – Concepts, Tricks & Applications

Permutation and Combination form the backbone of counting techniques in mathematics. These concepts are heavily tested in school exams and competitive exams because they measure logical thinking rather than direct calculation.

This guide is perfect for:

Class 11–12 students
Competitive exam aspirants (SSC, Banking, CAT basics)
Students confused between permutation and combination

1. Why Permutation & Combination Matter

Counting the number of possible arrangements and selections helps in probability, data analysis, and real-life decision making.

Password formation
Team selection
Seating arrangements
Lottery and probability calculations

2. Factorial – The Building Block

n! = n × (n−1) × (n−2) × … × 1

5! = 5 × 4 × 3 × 2 × 1 = 120

Factorial represents the number of ways to arrange n distinct objects.

3. What Is Permutation?

Permutation deals with arrangements where order matters.

Permutation (nPr) = n! / (n−r)!

Example:
Number of ways to arrange 3 books out of 5 books:

5P3 = 5! / 2! = 60

Permutation with Repetition

Number of permutations = nʳ

Using digits {1,2,3}, number of 2-digit numbers = 3² = 9

4. What Is Combination?

Combination deals with selection where order does not matter.

Combination (nCr) = n! / [r! (n−r)!]

Example:
Selecting 3 students from 5 students:

5C3 = 10

5. Key Difference: Permutation vs Combination

Permutation → Order matters
Combination → Order does not matter

6. Important Properties

nCr = nC(n−r)
nP r = nCr × r!
nC0 = nCn = 1

7. Important Exam Tricks

Trick 1: Words like “arrange”, “seat”, “rank” → Permutation

Trick 2: Words like “select”, “choose”, “form a team” → Combination

Trick 3: If repetition is allowed, think of powers instead of factorials

8. Common Mistakes Students Make

Using permutation instead of combination
Forgetting factorial in denominator
Ignoring repetition conditions
Overcomplicating simple problems

Exam Tip: Read the question twice. Identify keywords before applying formulas.

9. Applications in Probability

Permutation and combination are widely used to calculate:

Card probability
Dice problems
Selection probabilities
Arrangements under conditions

10. Practice With Solved Problems & Calculators

11. Final Thoughts

Permutation and combination may look formula-heavy, but once the logic is clear, they become some of the most scoring topics in mathematics.

Master the concept, apply exam tricks, and practice regularly for best results.

If this helped you understand the concept better, share it with your friends using the buttons below.