CAT Questions | CAT Permutation and Combination Questions

CAT Permutation and Combination question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Permutation, Combination, Probability, Counting and so on. In CAT Exam, one can generally expect to get 2~3 questions from CAT Permutation and Combination and Probability. CAT Permutation and Combination and Probability is an important topic in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. CAT Permutation and Combination: Counting natural numbers

   Sum of three Natural numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?

   1. 45
   2. 36
   3. 54
   4. 28

   Correct AnswerChoice B
   36

   Explanation

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2. CAT Permutation and Combination: Counting Whole Numbers

   Sum of three Whole numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?

   1. 66
   2. 78
   3. 72
   4. 56

   Correct AnswerChoice A
   66

   Explanation

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3. CAT Permutation and Combination: Counting - Toys and Boxes

   In how many ways 11 identical toys be placed in 3 distinct boxes such that no box is empty?

   1. 72
   2. 54
   3. 45
   4. 36

   Correct AnswerChoice C
   45

   Explanation

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4. CAT Permutation and Combination: Puzzle

   a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?

   1. 8
   2. 6
   3. 2
   4. 4

   Correct AnswerChoice D
   4

   Explanation

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5. CAT Permutation and Combination: Counting 7 Digit Numbers

   A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12?

   1. 11
   2. 12
   3. 10
   4. 22

   Correct AnswerChoice A
   11

   Explanation

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6. CAT Permutation and Combination: Alphabetical Order

   If all words with 2 distinct vowels and 3 distinct consonants were listed alphabetically, what would be the rank of “ACDEF’?

   1. 4716
   2. 4720
   3. 4718
   4. 1717

   Correct AnswerChoice C
   4718

   Explanation

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7. CAT Permutation and Combination: Basics

   If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?

   1. 3980
   2. 3700
   3. 3840
   4. 3780

   Correct AnswerChoice A
   3980

   Explanation

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8. CAT Permutation and Combination: Number System

   From the digits 2, 3, 4, 5, 6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?

   1. 36
   2. 60
   3. 84
   4. 72

   Correct AnswerChoice B
   60

   Explanation

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9. CAT Permutation and Combination: Numbers in Different Bases

   All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?

   1. 143
   2. 200
   3. 157
   4. 122

   Correct AnswerChoice A
   143

   Explanation

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10. CAT Permutation and Combination: Non-Zero Numbers

    All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will contain zero's?

    1. 25
    2. 20
    3. 35
    4. 45

    Correct AnswerChoice D
    45

    Explanation

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11. CAT Permutation and Combination: 5 Digit Numbers

    How many numbers of up to 5 digits can be created using the digits 1, 2, 3 and 5 each at least once such that they are a multiple of 15?

    1. 24
    2. 18
    3. 15
    4. 12

    Correct AnswerChoice D
    12

    Explanation Video Solution

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12. CAT Permutation and Combination: Numbers with Distinct Digits

    How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?

    1. 975
    2. 960
    3. 978
    4. 986

    Correct AnswerChoice C
    978

    Explanation Video Solution

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13. CAT Permutation and Combination: Alphabetical Order

    All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"?

    1. 36
    2. 74
    3. 42
    4. 86

    Correct AnswerChoice B
    74

    Explanation Video Solution

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14. CAT Probability: GP

    A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?

    1. \\frac{7}{10}\\)
    2. \\frac{15}{23}\\)
    3. \\frac{2}{3}\\)
    4. \\frac{11}{17}\\)

    Correct AnswerChoice B
    \\frac{15}{23}\\)

    Explanation Video Solution

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15. CAT Probability: Bayes Theorem

    Doctors have devised a test for leptospirosis that has the following property: For any person suffering from lepto, there is a 90% chance of the test returning positive. For a person not suffering from lepto, there is an 80% chance of the test returning negative. It is known that 10% of people who go for testing have lepto. If a person who gets tested gets a +ve result for lepto (as in, the test result says they have got lepto), what is the probability that they actually have lepto?

    1. \\frac{7}{10}\\)
    2. \\frac{8}{11}\\)
    3. \\frac{1}{3}\\)
    4. \\frac{1}{2}\\)

    Correct AnswerChoice C
    \\frac{1}{3}\\)

    Explanation Video Solution

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16. CAT Permutation and Combination: Rearranging Letters

    In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?

    1. 6720
    2. 2400
    3. 4320
    4. 1800

    Correct AnswerChoice B
    2400

    Explanation Video Solution

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17. CAT Permutation and Combination: Possible Integer Solutions

    2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b?

    1. 7
    2. 9
    3. 14
    4. 15

    Correct AnswerChoice A
    7

    Explanation Video Solution

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18. CAT Probability: Rearrangement of Letters

    If all the rearrangements of the word AMAZON are considered, what is the probability that M will feature between the 2As?

    1. \\frac{1}{3}\\)
    2. \\frac{1}{6}\\)
    3. \\frac{2}{5}\\)
    4. \\frac{3}{8}\\)

    Correct AnswerChoice A
    \\frac{1}{3}\\)

    Explanation Video Solution

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19. CAT Probability: Number Theory

    N is a 3-digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?

    1. \\frac{1}{5}\\)
    2. \\frac{11}{54}\\)
    3. \\frac{13}{64}\\)
    4. \\frac{13}{66}\\)

    Correct AnswerChoice C
    \\frac{13}{64}\\)

    Explanation Video Solution

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20. CAT Probability

    A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?

    1. \\frac{2}{5}\\)
    2. \\frac{1}{2}\\)
    3. \\frac{1}{3}\\)
    4. \\frac{2}{3}\\)

    Correct AnswerChoice D
    \\frac{2}{3}\\)

    Explanation Video Solution

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21. CAT Permutation and Combination: Rolling a Die

    I roll a die four times. In how many outcomes do we have two throws have the same number and the other two something different?

    1. 720
    2. 480
    3. 360
    4. 350

    Correct AnswerChoice A
    720

    Explanation

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22. CAT Permutation and Combination: Card Pack - Selection

    In how many ways can be select 5 cards from a card pack such that all 4 suits appear?

    1. 52728
    2. 405646
    3. 685464
    4. 4056

    Correct AnswerChoice C
    685464

    Explanation

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23. CAT Permutation and Combination: Rolling a Die

    I roll a die 4 times. In how many outcomes will each subsequent throw be greater that the previous one?

    1. 15
    2. 48
    3. 30
    4. 60

    Correct AnswerChoice A
    15

    Explanation

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24. CAT Permutation and Combination: 3 Digit Number

    Find 3 digit numbers such that product of their digits is a natural number less than 5?

    1. 11
    2. 15
    3. 13
    4. 17

    Correct AnswerChoice C
    13

    Explanation

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25. CAT Permutation and Combination: 3 Digit Number - Sum of Digits

    Find all 3 digit numbers such that sum of their digits is a whole number less than 5?

    1. 18
    2. 20
    3. 19
    4. 17

    Correct AnswerChoice B
    20

    Explanation

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26. CAT Permutation and Combination: Sum of Rearrangements

    What is sum of all rearrangements of the 4-digit number 3214?

    1. 66660
    2. 55554
    3. 60048
    4. 65024

    Correct AnswerChoice A
    66660

    Explanation

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27. CAT Permutation and Combination: Sum of Rearrangements

    What is sum of all rearrangements of the 4-digit number 3321?

    1. 29999
    2. 27777
    3. 28888
    4. 29997

    Correct AnswerChoice D
    29997

    Explanation

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28. CAT Permutation and Combination: Forming Triangles

    Of 22 points on a plane, 8 are on a straight line, 7 are on another straight line and 10 are on a third straight line. How many triangles can be drawn by connecting some three points from these 22?

    1. ²²C₃
    2. ²²C₃ - (⁸C₃+ ⁷C₃ +¹⁰C₃)
    3. ²²C₃ + (⁸C₃+ ⁷C₃ +¹⁰C₃)
    4. ⁸C₃+ ⁷C₃ +¹⁰C₃

    Correct AnswerChoice B
    ²²C₃ - (⁸C₃+ ⁷C₃ +¹⁰C₃

    Explanation

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29. CAT Probability: Selection

    A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag one ball is drawn, then what is the probability that the ball drawn is red?

    1. \\frac{39}{70}\\)
    2. \\frac{41}{70}\\)
    3. \\frac{29}{70}\\)
    4. \\frac{17}{35}\\)

    Correct AnswerChoice D
    \\frac{17}{35}\\)

    Explanation

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30. CAT Permutation and Combination: MANANA Rearrangment

    In how many ways can we rearrange the letters of the word MANANA such that no two A’s are adjacent to each other?

    1. 3 ! * ⁵C₃
    2. 4 ! * ⁴C₃
    3. 3 * ⁴C₃
    4. 3 ! * ⁴C₃

    Correct AnswerChoice C
    3 * ⁴C₃

    Explanation

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31. CAT Permutation and Combination: I between 2 A's

    How many ways are there for arranging letters of the word AMAZING such that the ‘I’ appears between the two ‘A’s?

    1. 5 ! ways
    2. 7 ! ways
    3. 8 ! ways
    4. 4 ! ways

    Correct AnswerChoice A
    5 ! ways

    Explanation

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32. CAT Permutation and Combination: Room Allocation

    In how many ways can 6 boys be allotted into 5 rooms such that no room is empty and all 6 boys are accommodated?

    1. 6 * 5 ! ways
    2. 7 * 5 ! ways
    3. 3 * 3 ! ways
    4. 15 * 5 ! ways

    Correct AnswerChoice D
    15 * 5 ! ways

    Explanation

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33. CAT Permutation and Combination: 3 Digit numbers > 500

    How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?

    1. 191
    2. 176
    3. 153
    4. 189

    Correct AnswerChoice B
    176

    Explanation

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The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.


IPMAT Rohtak Sample Paper Mock
IPMAT Indore Sample Paper Mock

Please note that the explanation button will take you to the IPMAT solution page.


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34. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Probability

    A bag contains 4 blue, 5 white and 6 green balls. Two balls are drawn at random. What is the probability that one ball is white?

    1. \\frac{10}{21}\\)
       
    2. \\frac{1}{2}\\)
    3. \\frac{3}{4}\\)
    4. \\frac{2}{35}\\)

    Correct AnswerChoice D
    \\frac{2}{35}\\)

    Explanation Video Solution

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35. IPMAT 2019 Question Paper - IPM Indore Quants,Probability

    From a pack of 52 cards, we draw one by one, without replacement. If f(n) is the probability that an Ace will appear at the n^th turn, then

    1. f(2) = \\frac{1}{13}\\) > f(3)
    2. \\frac{1}{13}\\) > f(2) > f(3)
    3. f(3) > f(2) = \\frac{1}{13}\\)
    4. f(2) = f(3) = \\frac{1}{13}\\)

    Correct AnswerChoice D
    f(2) = f(3) = \\frac{1}{13}\\)

    Explanation Video Solution

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36. IPMAT 2019 Question Paper - IPM Indore Quants,Probability

    A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

    1. \\frac{1}{6}\\)
    2. \\frac{1}{4}\\)
    3. \\frac{1}{5}\\)
    4. \\frac{1}{10}\\)

    Correct AnswerChoice C
    \\frac{1}{5}\\)

    Explanation Video Solution

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37. IPMAT 2019 Question Paper - IPM Indore Quants,Probability

    In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2,4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

    1. 4
    2. 4.667
    3. 4.333
    4. 3.667

    Correct AnswerChoice B
    4.667

    Explanation Video Solution

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The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.

1. CAT 2017 Question Paper Slot 1 - Permutation & Combination

   The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is

   1. 101
   2. 99
   3. 87
   4. 105

   Correct AnswerChoice B
   99

   Explanation Video Solution

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2. CAT 2017 Question Paper Slot 1 - Permutation & Combination

   Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle? (TITA)

   Correct Answer160
   

   Explanation Video Solution

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3. CAT 2017 Question Paper Slot 1 - Permutation & Combination

   In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

   1. 16
   2. 20
   3. 14
   4. 15

   Correct AnswerChoice A
   16

   Explanation Video Solution

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4. CAT 2017 Question Paper Slot 2 - Permutation & Combination

   In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens? [TITA]

   Correct Answer6
   

   Explanation Video Solution

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5. CAT 2017 Question Paper Slot 2 - Permutation & Combination

   How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position? [TITA]

   Correct Answer50
   

   Explanation Video Solution

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6. CAT 2018 Question Paper Slot 2 - Permutation & Combination

   In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is (TITA)

   Correct Answer1098
   

   Explanation Video Solution

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