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Permutation and combination practice questions for bank exams

By the PrepMatic team · Updated 9 Oct 2026 · 3 min read

Permutation and combination counts the ways of arranging or selecting items. A permutation cares about order (arranging letters, seating people), and a combination does not (choosing a committee). Bank exams use it in small problems that repeat a few set-ups, and it is the foundation for probability. The five questions below are at mains-arithmetic level.

Core rules

Factorials worth knowing: 4! = 24, 5! = 120, 6! = 720, 7! = 5,040, 8! = 40,320.

Five practice questions

Question 1

In how many ways can the letters of the word BANKING be arranged?

• A. 5,040
• B. 2,520
• C. 1,260
• D. 840

Question 2

A committee of 4 is to be chosen from 6 men and 4 women, with at least 2 women. In how many ways can it be formed?

• A. 90
• B. 105
• C. 115
• D. 210

Question 3

How many 3-digit even numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 if no digit is repeated?

• A. 60
• B. 90
• C. 120
• D. 180

Question 4

In how many ways can 6 persons sit around a circular table if two particular persons must sit together?

• A. 24
• B. 36
• C. 96
• D. 48

Question 5

From 5 consonants and 3 vowels, how many 4-letter arrangements, with no letter repeated, can be formed so that each contains exactly 2 vowels? (The arrangements need not be meaningful words.)

• A. 360
• B. 480
• C. 720
• D. 1,440

Answers and explanations

1. B. BANKING has 7 letters, and N appears twice. The number of arrangements is 7! ÷ 2! = 5,040 ÷ 2 = 2,520. The option 5,040 forgets the repeated N.
2. C. At least 2 women means three cases. Two women and two men: 6 × 15 = 90. Three women and one man: 4 × 6 = 24. Four women: 1. The total is 90 + 24 + 1 = 115. Check by complement: 10C4 = 210 ways in all, minus 15 with no woman and minus 80 with one woman, gives 115.
3. A. Fill the restricted place first. The units digit must be 2, 4 or 6, which is 3 ways. The hundreds digit then has 5 choices, and the tens digit has 4. So 3 × 5 × 4 = 60.
4. D. Treat the two persons as one block, giving 5 units around the table: (5 − 1)! = 24 ways. The two people can swap places inside the block, so multiply by 2 to get 48.
5. C. Choose 2 consonants out of 5: 10 ways. Choose 2 vowels out of 3: 3 ways. That gives 30 sets of four letters. Each set can be arranged in 4! = 24 ways, so the total is 30 × 24 = 720.

How to prepare permutation and combination

• Decide first: does order matter? Seating, passwords, digits and words are permutations. Committees, teams and hands of cards are combinations.
• Handle restricted places first. For even numbers, the units place goes first. For "starts with a vowel", the first place goes first.
• Block method for "together". Count the blocks, arrange them, then multiply by the order inside each block. For "never together", subtract the "together" count from the total.
• Use the complement for "at least". Total minus the unwanted cases is often shorter than adding three cases.
• Learn nCr values by symmetry. 10C7 equals 10C3, so you never compute the larger one. Know 5C2 = 10, 6C2 = 15 and 6C3 = 20 cold.
• Drill the standard variations: word arrangements, conditional selections, digit numbers and circular seating, all shown above.

Allow 60 to 90 seconds per question, because these are mains-style. Once you can count confidently, go to probability, which uses the same counting.

The full permutation and combination topic test is on PrepMatic (about 15 questions, 30 minutes). The Quantitative Aptitude guide lists where this topic appears, and the bank exam hub links each exam's pattern.

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