# CAT Questions | CAT Permutation and Combination Questions

###### CAT Quantitative Aptitude | CAT Permutations and Combinations, Probability

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

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

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

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

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

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

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

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

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

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

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

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

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

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. $\frac{8}{11}\\$ 3. $\frac{1}{3}\\$ 4. $\frac{1}{2}\\$ 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 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 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. $\frac{3}{8}\\$ 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. $\frac{13}{66}\\$ 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. $\frac{2}{3}\\$ 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 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 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 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 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 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 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 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

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. #### 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]

1. #### 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]

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

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)

1. #### 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

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

1. #### XAT 2020 Question Paper - QADI

Ashok has a bag containing 40 cards, numbered with the integers from 1 to 40. No two cards are numbered with the same integer. Likewise, his sister Shilpa has another bag containing only five cards that are numbered with the integers from 1 to 5, with no integer repeating. Their mother, Latha, randomly draws one card each from Ashok’s and Shilpa’s bags and notes down their respective numbers. If Latha divides the number obtained from Ashok’s bag by the number obtained from Shilpa’s, what is the probability that the remainder will not be greater than 2?

1. 0.91
2. 0.87
3. 0.94
4. 0.73
5. 0.8

2. #### XAT 2020 Question Paper - QADI

A box contains 6 cricket balls, 5 tennis balls and 4 rubber balls. Of these, some balls are defective. The proportion of defective cricket balls is more than the proportion of defective tennis balls but less than the proportion of defective rubber balls. Moreover, the overall proportion of defective balls is twice the proportion of defective tennis balls. What BEST can be said about the number of defective rubber balls in the box?

1. It is exactly 3
2. It is either 3 or 4
3. It is exactly 2
4. It is either 2 or 3
5. It is either 0 or 1

3. #### XAT 2019 Question Paper - QADI

A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag.There are two additional statement of facts available:
1. If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
2. If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.

Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

1. Statement 1 alone is suﬃcient, but statement 2 alone is not suﬃcient to answer the question.
2. Statement 2 alone is suﬃcient, but statement 1 alone is not suﬃcient to answer the question.
3. Statements 1 and 2 together are not suﬃcient, and additional data is needed to answer the question.
4. Each statement alone is suﬃcient to answer the question.
5. Both statements taken together are suﬃcient to answer the question, but neither statement alone is suﬃcient.

4. #### XAT 2018 Question Paper - QADI

A coin of radius 3 cm is randomly dropped on a square floor full of square shaped tiles of side 10 cm each. What is the probability that the coin will land completely within a tile? In other words, the coin should not cross the edge of any tile.

1. 0.91
2. 0.5
3. 0.49
4. 0.36
5. 0.16

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

1. #### IPMAT 2020 Sample Paper - IPM Rohtak Quants

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. $\frac{2}{35}\\$ 2. #### IPMAT 2020 Question Paper - IPM Rohtak Quants Five racquets needs to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical? 1. 24 2. 25 3. 27 4. 26 3. #### IPMAT 2020 Question Paper - IPM Rohtak Quants How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time? 1. 1988 2. 1976 3. 1966 4. 1956 4. #### IPMAT 2020 Question Paper - IPM Rohtak Quants There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected? 1. 3388 2. 3376 3. 3366 4. 3327 5. #### IPMAT 2020 Question Paper - IPM Rohtak Quants Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike? 1. 4845 2. 4800 3. 4855 4. 4955 6. #### IPMAT 2020 Question Paper - IPM Rohtak Quants A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw? 1. 60 2. 40 3. 64 4. 82 7. #### IPMAT 2020 Question Paper - IPM Rohtak Quants Can you calculate in how many ways can 7 tennis players can be seated in a circular order? 1. 330 2. 730 3. 720 4. 820 8. #### IPMAT 2020 Question Paper - IPM Rohtak Quants Please calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set? 1. 60 2. 72 3. 56 4. 75 9. #### IPMAT 2020 Question Paper - IPM Indore Quants out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is __________. 10. #### IPMAT 2020 Question Paper - IPM Indore Quants The probability that a randomly chosen factor of 1019 is a multiple of 1015 is 1. $\frac{1}{25}$ 2. $\frac{1}{12}$ 3. $\frac{1}{20}$ 4. $\frac{1}{16}$ 11. #### IPMAT 2020 Question Paper - IPM Indore Quants A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is 1. $\frac{4}{9}$ 2. $\frac{5}{9}$ 3. $\frac{4}{15}$ 4. $\frac{2}{15}$ 12. #### IPMAT 2019 Question Paper - IPM Indore Quants 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 nth 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}\\$ 13. #### IPMAT 2019 Question Paper - IPM Indore Quants 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. $\frac{1}{10}\\$ 14. #### IPMAT 2019 Question Paper - IPM Indore Quants 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 ###### Prepare for CAT 2022 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube #### Other useful sources for Permutation and Combination Questions | Probability Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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