Permutation & Combination — Banking Quant Notes Ch. 22

Introduction

Permutation counts arrangements where order matters; Combination counts selections where order doesn't matter. Getting this distinction right at the start of a question is the single biggest factor in solving it correctly.

Core Formulas

Concept	Formula
Factorial	n! = n × (n−1) × (n−2) × ... × 1
Permutation (arrangement)	ⁿPᵣ = n! / (n−r)!
Combination (selection)	ⁿCᵣ = n! / [r! × (n−r)!]
Circular arrangement	(n−1)! for n distinct objects around a circle

Q. In how many ways can 3 letters be arranged out of the word "MOBILE" (6 distinct letters)?

This is an arrangement (order matters) → ⁶P₃ = 6!/(6−3)! = 6×5×4 = 120 ways.

Q. In how many ways can a committee of 3 be selected from 5 men and 4 women, if the committee must have exactly 2 men and 1 woman?

This is selection (order doesn't matter) → Choose 2 men from 5: ⁵C₂ = 10. Choose 1 woman from 4: ⁴C₁ = 4. Total ways = 10 × 4 = 40 ways.

⚠️ Key Insight: Ask "does the order of selection change the outcome?" — if yes (like arranging people in seats), use Permutation; if no (like forming a committee), use Combination.

💡 Exam Tip: For "at least" or "at most" selection problems, break the count into separate cases (e.g., exactly 1, exactly 2, ...) and add the combinations — don't try to force a single formula.

✅ Practice Focus: Distinguishing permutation vs combination · Word/letter arrangement problems · Committee/team selection with gender or category restrictions.

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