Permutation and Combination in Bank Exams
In SBI PO and IBPS PO prelims and mains, permutation and combination (P&C) appears as 1 to 2 direct questions and also inside probability questions. The whole topic rests on one decision: does order matter? If yes, it is a permutation (arrangement); if no, it is a combination (selection).
Key takeaway: nPr = n!/(n − r)!. nCr = n!/[r!(n − r)!]. Words with repeated letters: n!/(p!·q!·…). Circular arrangement of n people: (n − 1)!. Necklace/garland: (n − 1)!/2. "At least one" = total − none. "Together" = tie as one unit, then arrange inside.
Every answer below was checked by brute force in Python (actual listing of all arrangements), not just by formula. Use it together with our probability questions for bank exams note.
Permutation and Combination Formulas (Table)
| Concept | Formula |
|---|---|
| Factorial | n! = n × (n − 1) × … × 1 ; 0! = 1 |
| Permutations of r from n | nPr = n!/(n − r)! |
| Combinations of r from n | nCr = n!/[r!(n − r)!] |
| Link | nPr = nCr × r! |
| Symmetry | nCr = nC(n − r) |
| Arrange n things with p alike, q alike | n!/(p! × q!) |
| Circular arrangement of n distinct people | (n − 1)! |
| Necklace / garland (clockwise = anticlockwise) | (n − 1)!/2 |
| Handshakes among n people | nC2 |
| Diagonals of an n-sided polygon | nC2 − n |
| Triangles from n points, m collinear | nC3 − mC3 |
| Selecting at least one from n | 2ⁿ − 1 |
Solved Permutation and Combination Questions
- Words from BANKING (N repeats): 7!/2! = 2,520.
- BANKING with vowels together (A, I as one unit): 6!/2! × 2! = 720.
- Words from LEADER (E repeats): 6!/2! = 360.
- Words from MISSISSIPPI: 11!/(4! × 4! × 2!) = 34,650.
- Committee of 3 men and 2 women from 6 men and 5 women: 6C3 × 5C2 = 20 × 10 = 200.
- 4-member team with at least one woman from 5 men and 4 women: 9C4 − 5C4 = 126 − 5 = 121.
- 6 people around a round table: (6 − 1)! = 120. With two particular people together: 4! × 2 = 48.
- 5 boys and 3 girls in a row, all girls together: 6! × 3! = 4,320.
- 5 boys and 3 girls in a row, no two girls together: arrange boys 5! = 120, then choose 3 of the 6 gaps for girls in order, 6P3 = 120: total 14,400.
- 4-digit numbers from digits 0-9 without repetition: 9 × 9 × 8 × 7 = 4,536.
- 3-digit even numbers from 1, 2, 3, 4, 5 without repetition: units digit 2 or 4 (2 ways) × 4 × 3 = 24.
- Handshakes among 12 people: 12C2 = 66. Diagonals of a decagon: 10C2 − 10 = 35. Triangles from 10 points with 4 collinear: 10C3 − 4C3 = 116. Necklace of 7 different beads: 6!/2 = 360.
Tricks for P&C Questions
- Keywords: arrange, order, rank, word, number, password → permutation. Choose, select, team, committee, group → combination.
- "Together" → glue; "not together" → total − together (or use the gap method for "no two together").
- Zero in digit questions: fix the first digit first (it cannot be 0), then fill the rest.
- Round table: fix one person, arrange the rest, so (n − 1)!.
- Check small cases: for 3 or 4 items, list them quickly to confirm the formula.
Common Mistakes in Permutation and Combination
- Using nCr when order matters (e.g. president and secretary are different posts: use nPr).
- Forgetting to divide by repeated letters (BANKING has two Ns).
- Using n! instead of (n − 1)! for circular seating.
- Forgetting the internal arrangement (×2!, ×3!) of a glued group.
- Allowing 0 as the first digit of a number.
Permutation and Combination FAQs
What is the difference between permutation and combination?
Permutation counts arrangements where order matters (nPr = n!/(n − r)!). Combination counts selections where order does not matter (nCr = n!/[r!(n − r)!]).
How many ways can n people sit around a round table?
(n − 1)! ways, because rotations of the same seating are counted once. For a necklace or garland it is (n − 1)!/2.
How do you solve "at least one" questions?
Find the total number of selections and subtract the selections with none of the required type. Example: at least one woman in a 4-member team from 5 men and 4 women = 9C4 − 5C4 = 121.
Is permutation and combination asked in SBI PO?
Yes, as 1 to 2 direct questions in prelims or mains, and as the counting step inside probability questions.
Practice Next
- Mock tests: IBPS PO Quantitative Aptitude Sectional Mock Test 01, IBPS PO Quantitative Aptitude Sectional Mock Test 02 and IBPS Clerk Numerical Ability Sectional Mock Test 03.
- Related notes: probability questions for bank exams, circular seating arrangement tricks, mixture and alligation questions for bank exams and simplification tricks for bank exams.
- Browse all study notes.