CMAT Permutations & Combinations Practice Questions With Solutions

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CMAT Quantitative Techniques and Data Interpretation Permutations & Combinations Practice Questions

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Question 1.

The probability that the birthdays of 4 different persons will fall in exactly two calendar months is :

$\frac{77}{1728}$

$\frac{17}{87}$

$\frac{11}{144}$

$\frac{3}{144}$

Question 2.

A consignment of 15 wrist watches contains 4 defectives. The wrist watches are selected at random, one by one and examined . The ones examined are not replaced back. What is the probability that ninth one examined is the last defective?

$\frac{11}{195}$

$\frac{8}{195}$

$\frac{17}{195}$

$\frac{16}{195}$

Question 3.

In how many ways can the following prizes be given away to a class of 30 students, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English?

$\frac{30!}{4!}$

$(30)^{4} \times (29)^{4}$

$(30)^{3} - 1$

$(30)^{4} \times 1 (29)^{2}$

Question 4.

20 girls, among whom are A and B sit down at a round table. The probability that there are 4 girls between A and B is

$\frac{2}{19}$

$\frac{6}{19}$

$\frac{13}{19}$

$\frac{17}{19}$

Question 5.

There are 10 stations on a railway line. The number of different journey tickets that are require by the authorities , is

Question 6.

Find the number of permutations that can be made from the letters of the word OMEGA, if the vowels occupy odd places.

12 ways

6 ways

16 ways

20 ways

Question 7.

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 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 8.

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 9.

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 10.

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

Great Job! continue working on more practice questions?

Question 1.

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 2.

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 3.

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 4.

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 5.

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 6.

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 7.

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

168

120

Question 8.

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 9.

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 10.

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

Great Job! continue working on more practice questions?

CMAT Permutations & Combinations Practice Questions With Solutions

CMAT Quantitative Techniques and Data Interpretation Permutations & Combinations Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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