Mathematics · Class 11
Permutations and Combinations
Learn Permutations and Combinations with notes, examples, and practice questions.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Counting techniques for arrangements (order matters) and selections (order doesn't). Foundation for probability and binomial theorem.
Formulas
Factorial
n! = n×(n−1)×…×1; 0!=1
Permutation
ⁿPᵣ = n!/(n−r)!
Combination
ⁿCᵣ = n!/[r!(n−r)!]
Relation
ⁿPᵣ = ⁿCᵣ × r!
When to Use
- Permutation: rank, seating order, PIN codes
- Combination: committees, teams, choosing items
- Circular permutation: (n−1)! for distinct objects
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
⁸P₃
Evaluate.
- 18×7×6
Answer
336
⁸C₃
Evaluate.
- 1336/6
Answer
56
Key Points to Remember
- ✓ Order matters → permutation
- ✓ Order irrelevant → combination
- ✓ ⁿCᵣ = ⁿCₙ₋ᵣ
Exam Tips
- • Identify if positions are distinct
- • Use complement counting when easier
Practice MCQs — Permutations and Combinations
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
0! equals: