IBPS Clerk · Bite-size lessons

Permutation and Combination

About 6 min · Numerical Ability · English

Time worked out from the lesson's 381 words at 150 words a minute, plus a minute for each question.

Permutation and Combination forms the foundation of counting problems in IBPS Clerk Prelims. The marks here are essentially "free" for well-prepared candidates.

Key ideas

• Fundamental Counting Principle: If one task can be done in m ways and another in n ways, both tasks together can be done in m × n ways. This is the backbone of all counting problems.
• Factorial (n!): The product of all positive integers from 1 to n. Example: 5! = 5 × 4 × 3 × 2 × 1 = 120. Remember: 0! = 1 and 1! = 1.
• Permutation (ⁿPᵣ): Number of ways to arrange r items from n distinct items where order matters. Use when the problem asks about "arrangements," "sequences," or "positions."
• Combination (ⁿCᵣ): Number of ways to select r items from n distinct items where order doesn't matter. Use when the problem asks about "selecting," "choosing," or "forming groups."
• Permutation with Repetition: When items can repeat, n choices for each of r positions gives nʳ arrangements.

Watch out for

• Confusing when order matters: Students use permutation for committee selection (where order doesn't matter) → Fix: Ask yourself, "Does swapping two selected items create a different outcome?" If no, use combination.
• Forgetting constraints on first digit: When forming numbers, the first digit cannot be 0 → Fix: Always fill the most restricted position first (hundreds place), then count remaining positions.
• Calculation errors with factorials: Computing 7!/(4! × 3!) by expanding everything → Fix: Cancel common terms immediately. 7!/(4! × 3!) = (7 × 6 × 5)/(3 × 2 × 1).

Quick reference

• Order matters → Permutation (ⁿPᵣ) | Order doesn't matter → Combination (ⁿCᵣ)
• ⁿPᵣ = n!/(n-r)! and ⁿCᵣ = n!/[r!(n-r)!]
• Fundamental Principle: Multiply choices at each independent step
• "At least" problems: Break into cases or use Total − Unwanted cases
• First digit ≠ 0: Always handle the hundreds place separately when forming numbers

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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