Is Probability and Combinatorics important for CMAT?

Yes, Probability and Combinatorics is an important topic in the Quantitative Aptitude section of CMAT. It evaluates a candidate's mathematical reasoning, analytical skills, and ability to solve counting and probability-based problems.

How many Probability and Combinatorics questions can appear in CMAT?

The number of Probability and Combinatorics questions varies each year. CMAT does not prescribe a fixed number of questions from any specific Quantitative Aptitude topic.

What types of Probability and Combinatorics questions are asked in CMAT?

CMAT may include questions on permutations, combinations, basic probability, counting principles, arrangements, selections, and event-based probability problems.

How can I prepare for Probability and Combinatorics questions in CMAT?

Build a strong understanding of permutations, combinations, and probability concepts, practice a wide range of problems regularly, revise important formulas, and solve previous year questions and mock tests.

Are CMAT Probability and Combinatorics questions difficult?

Probability and Combinatorics questions in CMAT are generally of moderate difficulty. Candidates with strong conceptual clarity and regular practice can solve them efficiently.

How do Cracku's CMAT Probability and Combinatorics Questions help in preparation?

Cracku's CMAT Probability and Combinatorics Questions provide topic-wise practice, detailed solutions, and exam-oriented problems that help candidates improve conceptual understanding, speed, and accuracy for CMAT 2027.

CMAT Probability, Combinatorics Questions

Question 1

Given below are two statements :
A number of distinct 8-letter words are possible using the letters of the word SYLLABUS. If a word in chosen at random, then

Statement I: The probability that the word contains the two S's together is $$\frac{1}{4}$$

Statement II : The probability that the word begins and ends with L is $$\frac{1}{28}$$.
In the light of the above statements, choose the correct answer from the options given below

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Question 2

What is the probability of getting a sum of 22 or more when four dice are thrown?

$$\frac{5}{432}$$

$$\frac{4}{648}$$

$$\frac{1}{144}$$

$$\frac{7}{36}$$

Question 3

Given below are two statements :
Statement I: The number of ways to pack six copies of the same book into four identical boxes where a box can contain as many as six books, is 9.
Statement II: The minimum number of students needed in a class to guarantee that there are at least six students whose birthday fall in the same month, is 61 .
In the light of the above statements, choose the correct answer from the options given below.

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Question 4

Given below are two statements:
Statement I: Let A and B be two events such that P(A) = 0.6, P(B) = 0.2 and P(AB) = 0.5. Then P(AC BC) = $$\frac{3}{10}$$
Statement II: Let A and B be two events such that P(A) = 0.2, P(B) = 0.4 and P(AUB) = 0.6. The.n P(AB) = $$\frac{3}{10}$$
In the fight of the above statements choose the most appropriate answer from the options given below:

Both Statement I and Statement II are correct

Both Statement I and Statement II are incorrect

Statement I is correct but Statement II is incorrect

Statement I is incorrect but Statement II is correct

None of the above

Question 5

Given below are two statements:
Statement I : A bag captains 10 white and 10 red face masks which are all mixed up. The fewest number of face masks you can take from a bag without looking and be sure to get a pair of the same color is 3.
Statement II: The minimum number of students needed in a class to guarantee that there are at least 6 students whose birthdays fall in the same month, is 61.
In the light of the above statements, choose the most appropriate answer from the option given below:

Both Statement I and Statement II are correct

Both Statement I and Statement II are incorrect

Statement I is correct but Statement II is incorrect

Statement I is incorrect but Statement II is correct

Question 1

A bag contains 6 red balls, 11 yellow balls and 5 pink balls. If two balls are drawn at a random from the bag, one after another. What is the probability that the first ball drawn was red and the second ball drawn was yellow in colour?

$$\frac{3}{14}$$

$$\frac{5}{7}$$

$$\frac{1}{7}$$

$$\frac{1}{14}$$

Question 2

In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls and 1 green ball is :

$$\frac{21}{46}$$

$$\frac{25}{117}$$

$$\frac{3}{25}$$

$$\frac{1}{50}$$

Question 1

Given below are two statements
Statement I : A committee of 4 can be made out of 5 men and 3 women containing at least one woman in 65 ways.
Statement II : The number of words which can be formed using letters of the word ARRANGE' so that vowels always occupy even place is 36.

In light of the above statements, choose the correct answer from the options given below

Both Statement I and Statement II are true

Both Statement I and Statement II are false

Statement I is true but Statement II is false

Statement I is false but Statement II is true

Question 2

How many ten-digit numbers can be formed using all the digits of 2435753228 such that odd digits appear only in even places?

$$2!3!5!$$

$$(5!)^{2}$$

$$\frac{(5!)^{2}}{3!}$$

$$\frac{(5!)^{2}}{3!(2!)^{2}}$$

Question 3

Match List I with List II.
Let A and B be events with $$P(A)=\frac{2}{3}, P(B)=\frac{1}{2}$$ and $$P(A\cap B)=\frac{1}{3}$$

(Here c stands for complement)
Choose the correct answer from the options given below:

(A)-(II), (B)-(III), (C)-(IV), (D)-(I)

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

(A)-(I), (B)-(III), (C)-(IV), (D)-(II)

(A)-(II), (B)-(IV), (C)-(III), (D)-(I)

Question 4

During the next year, the probability that a Company A releases a mobile is 0.7. The probability that mobile is a success. given that it is released by the Company is 0.8. The probability that a mobile is a success and released by a Company B is 0.28. A mobile released by either Company A or Company B during the next one year is a success. Find the probability that it is released by Company A.

$$\frac{1}{3}$$

$$\frac{1}{2}$$

$$\frac{2}{3}$$

$$\frac{3}{4}$$

Question 1

In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?

5041

5040

11670

11760

Question 2

Brother and sister both appear for an interview. The probability of the selection of brother is $$\frac{1}{8}$$ while the probability of rejection of sister is $$\frac{4}{5}$$ What is the probability that only one of them is selected ?

$$\frac{11}{40}$$

$$\frac{7}{40}$$

$$\frac{5}{13}$$

$$\frac{1}{10}$$

Question 3

There are six teachers. Out of them, two teach physics, other two teach Chemistry and the rest two teach Mathematics. They have to stand in a row such that Physics, Chemistry and Mathematics teachers are always in a set. The numberof ways in which they can do, is :

Question 4

In how many different ways, can the letters of the words EXTRA be arranged so that the vowels are never together ?

168

120

Question 1

There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or person 2. Task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done ?

360

192

144

180

Question 2

What is the probability of drawing a king or a heart from a deck of cards ?

1/13

1/52

17/15

4/13

Question 3

In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or more.

5/18

5/12

2/7

2/36

Solution

When a pair of dice are thrown simultaneously the maximum sum possible is 12.

The possible cases of getting a sum of 9 are:

dice 1 dice 2

four five.....................(1)

five four.....................(2)

six three....................(3)

three six.......................(4)

So a total of 4 cases are possible

The possible cases of getting a sum of 10 are:

dice 1 dice 2

four six......................(1)

six four.....................(2)

five five.....................(3)

So a total of 3 cases are possible

The possible cases of getting a sum of 11 are:

dice 1 dice 2

five six...................(1)

six five..................(2)

So a total of 2 cases are possible

The possible cases of getting a sum of 12 are:

dice 1 dice 2

six six.....................(1)

So a total of 1 case is possible.

Total number ways of getting a sum of 9 or more = 4 + 3 + 2 + 1 = 10 ways

Total outcomes when two dice are rolled simultaneously = 6 * 6 = 36 ways

Probability of getting a sum of 9 or more = Expected number of outcomes/ Total outcomes

= $$\frac{10}{36}$$

= $$\frac{5}{18}$$

Question 4

A management institute has 6 senior professors and 4 junior professors, 3 professors are selected at random for a government project. The probability that at least one of the junior professors would get selected is :

2/3

1/5

5/6

1/6

Question 1

What is the probability of getting a ‘nine’ or ‘ten’ on a single throw of two dice?

2/9

7/36

1/5

2/7

Solution

Probability = Expected number of outcomes/ Total number of outcomes.

Total number of outcomes we get in a single throw of two dice = $$6\times 6$$ = 36.

Possible cases of getting 'nine' in a single throw of two dice:

dice 1 dice 2

three six..................(1)

six three................(2)

four five..................(3)

five four...................(4)

So, total of 4 cases.

Possible cases of getting 'ten' in a single throw of two dice:

dice 1 dice 2

four six.....................(1)

six four....................(2)

five five....................(3)

So, total of 3 cases.

Expected number of outcomes = Total possible cases of getting 'nine' or 'ten' in a single throw of two dice = 4 + 3 = 7 .

So, Probability = $$\frac {7} {36}$$

Question 2

In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one black?

1/16

28/55

3/8

8C2 / 4C1

Question 3

Three coins are tossed in the air and two of the coins land with tails face upwards. What are the chances on the next toss of the coins that at least two of the coins will land with the tails facing upwards?

50%

25%

75%

100%

Question 4

In how many different ways can 3 red balls, 2 blue balls and 4 yellow balls be arranged so that the balls of the same color come together? (Consider the balls are not identical except for the colour)

1742

1732

1728

1750

CMAT Probability, Combinatorics Questions

Probability and Combinatorics Questions are important topics in the Quantitative Aptitude section of CMAT 2027. These questions test a candidate's understanding of counting techniques, arrangements, selections, and the likelihood of events. Concepts such as permutations, combinations, and probability are used to assess logical thinking, analytical ability, and mathematical reasoning. A strong grasp of these topics enables candidates to solve complex problems efficiently and accurately. Aspirants preparing for the CMAT 2027 Exam should study Probability and Combinatorics thoroughly as part of the CMAT Syllabus to strengthen their Quantitative Aptitude preparation.

Regular practice of Probability and Combinatorics Questions helps candidates improve problem-solving speed, develop systematic approaches to counting problems, and apply probability concepts correctly. Since these questions often require conceptual clarity rather than lengthy calculations, consistent practice is essential for achieving accuracy. Solving questions from CMAT Previous Papers helps candidates understand the types and difficulty level of questions asked in previous years. Additionally, attempting a CMAT Mock Test enables aspirants to assess their preparation, improve time management, and build confidence for CMAT 2027.