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Permutations and Combinations Questions for CAT

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Verified questions549
Worked solutions in practice mode41 from CAT papers
139 easy251 medium159 hard

Permutation and Combination is where CAT questions are shortest to read and longest to solve. The difficulty is almost never the counting formula, it is deciding whether order matters, whether repetition is allowed, and whether the cases overlap. Candidates who go wrong here usually went wrong in the first sentence of their working, not the last. Practising many small variants is the only reliable way to build the habit of classifying before counting.

20 free Permutations and Combinations questions

1EasyTITA

In how many ways can three points be chosen from 10 points on the circumference of a circle and its center so as to form a triangle?

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2EasyTITA

How many 8-letter words can be formed using the letters in the word TRUTHFUL?

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3EasyMCQ

There are 4 qualifying exams to enter Oxford: RAT, BAT, SAT, PAT. - Engineer can't go via BAT or SAT → 2 ways: RAT, PAT - CA can go via RAT, BAT, PAT → 3 ways - CA has 3 ways to become CA → total = 3×3=93 \times 3 = 9 Engineer → 2 ways CA → 9 ways Find ratio (Engineer:CA)

  1. A

    3:23:2

  2. B

    2:32:3

  3. C

    2:92:9

  4. D

    9:29:2

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4EasyMCQ

In how many ways can 12 papers be arranged if the best and the worst paper never come together?

  1. A

    12!/2!12!/2!

  2. B

    12!−11!12! - 11!

  3. C

    (12!−11!)/2(12! - 11!)/2

  4. D

    12!−2⋅11!12! - 2 \cdot 11!

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5EasyMCQ

How many different words can be formed with the word KISMAT with conditions that the letters S & M are always together and the word always starts with S?

  1. A

    24

  2. B

    48

  3. C

    720

  4. D

    120

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6EasyMCQ

A reputed paint company plans to award prizes to its top three salespersons, with the highest prize going to the top salesperson, the next highest prize to the next salesperson and a smaller prize to the third-ranking salesperson. If the company has 1515 salespersons, how many different arrangements of winners are possible (Assume there are no ties)?

  1. A

    1728

  2. B

    2730

  3. C

    3856

  4. D

    1320

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7MediumMCQ

Find the total numbers of 9-digit numbers that can be formed all having different digits.

  1. A

    10P9{}^{10}P_9

  2. B

    9!

  3. C

    10!−9!10! - 9!

  4. D

    9×9!9 \times 9!

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8MediumMCQ

In the above question, what is the minimum number of shoes required to be drawn out to get at least 1 pair of correct shoes (either white or black)?

  1. A

    12

  2. B

    7

  3. C

    13

  4. D

    18

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9MediumMCQ

The crew of an 8-member rowing team is to be chosen from 12 men, of which 3 must row on one side only and 2 must row on the other side only. Find the number of ways of arranging the crew with 4 members on each side.

  1. A

    40,320

  2. B

    30,240

  3. C

    60,480

  4. D

    None of these

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10MediumMCQ

If the number of ways in which we can distribute 1414 identical bats, 88 identical balls, and 33 identical gloves among 3 children, ensuring that each child receives at least 33 bats and 22 balls is nn. What is the probability that dividing nn by a randomly chosen number from the range 22 to 99 (inclusive) will result in a non-zero remainder?

  1. A

    1/8

  2. B

    1/4

  3. C

    3/4

  4. D

    3/8

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11MediumMCQ

Let S be the set of four-digit numbers formed by the digits {1,2,3,4} using each digit exactly once such that exactly one odd position is occupied by an odd digit. What is the sum of the digits in the rightmost position of the numbers in S?

  1. A

    36

  2. B

    40

  3. C

    44

  4. D

    48

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12MediumMCQ

If you visit a restaurant and need to pay a bill of Rs.216 using only 1, 10, and 100 rupee notes, how many different ways can you make the payment?

  1. A

    20

  2. B

    24

  3. C

    36

  4. D

    40

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13MediumMCQ

In question 27, find the number of ways in which only two letters go in the wrong envelopes?

  1. A

    4

  2. B

    5

  3. C

    6

  4. D

    3

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14MediumMCQ

17P_r = 57120, 17P_{r-1} = 4080. Find the value of r?

  1. A

    4

  2. B

    5

  3. C

    6

  4. D

    7

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15HardMCQ

The number of ways in which four particular persons A,B,C,DA, B, C, D and six more persons can stand in a queue so that AA always stands before BB, BB always before CC and CC always before DD is

  1. A

    10!/4!10!/4!

  2. B

    10P4{}^{10}P_4

  3. C

    10C4{}^{10}C_4

  4. D

    None of these

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16HardMCQ

Seven different objects must be divided among three people. In how many ways can this be done if at least one of them gets exactly 1 object?

  1. A

    2484

  2. B

    1218

  3. C

    729

  4. D

    None of these

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17HardMCQ

There are 88 steps from the ground floor of a building to the first floor. A person can climb either 11 step at a time or 22 steps at a time or 33 steps at a time. What is the total number of ways in which the person can climb the stairs to reach the first floor from the ground floor?

  1. A

    81

  2. B

    102

  3. C

    149

  4. D

    164

  5. E

    221

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18HardTITA

In how many ways can the letters of the word 'ARRANGEMENT' be arranged so that no two A’s are together?

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19HardMCQ

The number of circles that can be drawn out of 10 points of which 7 are collinear is

  1. A

    130

  2. B

    85

  3. C

    45

  4. D

    Cannot be determined

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20HardTITA

Four married couples (8 distinct people) are to be seated around a circular table. In how many ways can they be seated so that no husband sits next to his wife?

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See the 41 CAT PYQs on Permutations and CombinationsActual papers, 2017–2025, organised by year and slot

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Permutations and Combinations for CAT, answered

What CAT asks in Permutations and Combinations, the mistakes that cost the most marks, and how to practise it.

Arrangements and selections with and without repetition, circular arrangements, arrangements with identical objects, distributing objects into groups, and counting problems that require complementary counting or inclusion-exclusion rather than a direct formula.

Ask whether swapping two chosen items produces a genuinely different outcome. If it does, order matters and it is a permutation; if not, it is a combination. Answering that question explicitly before writing anything prevents most errors in this topic.

Usually double-counting overlapping cases, or treating identical objects as distinct. When a case-based answer feels close but wrong, check the cases for overlap before checking the arithmetic, the arithmetic is rarely the problem.

Every question here has been checked against a worked solution before being published, and anything without a complete solution is not shown at all. The bank mixes questions written for CAT-level practice with questions from actual CAT papers; the previous-year questions are collected separately under CAT PYQs. The solutions themselves open in practice mode once you sign up, which is free.