Top 160 Permutation and Combination questions [ 100% FREE ]

Welcome, dear readers! If you’ve ever scratched your head over Permutation and Combination questions, you’re not alone. They form a fundamental pillar in the world of mathematics and logic. But what exactly are these Permutation and Combination questions? A permutation is how you can arrange certain things in a definite order, whereas a combination deals with selecting items without fussing over the order. Now, why are these questions so essential? The answer lies in the vast applications of permutation and combination in our daily life.

Permutation and Combination questions are omnipresent, especially in the competitive realm. For those preparing for competitive exams, having a grip on Permutation and Combination questions is a must. Are you aiming to crack exams like the CAT? Well, understanding permutation and combination for CAT can indeed give you an edge. Not only that, but these concepts also find their relevance in aptitude tests, where permutation and combination aptitude questions test one’s problem-solving ability.

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The world of permutation and combination doesn’t restrict itself to the CAT or aptitude tests. These concepts are frequently tested in various government exams like Bank, SSC, Railways, and more. So, it’s of paramount importance for aspirants to understand and master Permutation and Combination questions.

In this article, not only will you find a treasure trove of Permutation and Combination questions, but you’ll also gain access to detailed explanations that will simplify these intricate concepts. It doesn’t matter if you are just starting out or need advanced permutation and combination problems; this compilation will serve all your needs.

In conclusion, we encourage all our readers to dive deep into the world of Permutation and Combination questions. With practice and understanding, no problem is too big to solve. Whether you’re seeking information in Hindi, prepping for the CAT, or need a handy permutation and combination pdf for reference, we’ve got you covered. Happy learning!

Top 160 Permutation and Combination questions:

31. Two unbiased coins are tossed. What is the probability of getting exactly two heads?

A. 1/2
B. 1/3
C. 1/4
D. 3/4
E. None of these

Option “C” is correct.

Total event={HH, HT, TH, TT}=4

Possible=HH=1

Required probability=1/4

32. A bag contains 5 red balls and 7 blue balls. Find the probability to choose 2 balls in the same color.

A. 1/66
B. 31/66
C. 29/66
D. 1/22
E. 1/33

Option “B” is correct.

Probability = (5C2 + 7C2)/12C2

= [(5 * 4) + (7 * 6)] / (12 * 11)

= 31/66

33. If the box contains 4 red balls and 3 green balls, what is the probability of picking two balls of the same color?

A. 2/5
B. 3/7
C. 4/9
D. 1/5
E. None of these

Option “B” is correct.

Required probability= (4C2+3C2)/7C2

=18/42

=3/7

34. What is the probability of selecting 2 red balls from the bag containing 4 yellow balls and 5 red balls?

A. 1/9
B. 1/6
C. 2/9
D. 5/18
E. None of these

Option “D” is correct.

Required probability = 5C2 / 9C2

= 20/72

= 5/18

35. If the bag contains 3 apples and 4 orange, what is the probability of choosing two oranges?

A. 1/7
B. 2/7
C. 3/7
D. 4/7
E. None of these

Option “B” is correct.

Total fruits = 4 + 3 = 7

Required probability = 4C2/7C2   

= 4 * 3/7 * 6

= 2/7

36. Find the number of ways can the word “COMPASS” can be arranged, so that the vowels always come together.

A. 120
B. 180
C. 360
D. 720
E. None of these

Option “D” is correct.
Required number of ways = 6! * 2!/2! = 6 * 5 * 4 * 3 * 2 = 720
37. In how many ways word “SUMMITS” be arranged in that all vowels and consonants come together?

A. 120
B. 240
C. 720
D. 360
E. 180

Option “A” is correct.

Number of vowels = U, I = 2

Remaining letters = S, M, M, T, S = 5

Number of ways = 2! * 5! * 2!/(2! * 2!)

= 120

38. A teacher and head master are chosen out of a group having 15 persons. How many ways are there?

A. 120
B. 180
C. 210
D. 240
E. 280

Option “C” is correct.
Total number of ways=15 * 14=210
39. Two students are selected from 8 students. How many ways are there to achieve this?

A. 68
B. 64
C. 56
D. 52
E. None of these

Option “C” is correct.
Number of ways=8 * 7=56
40. In how many different ways can the letters of the word “ELECTION” be arranged ?

A. 13440
B. 40320
C. 20160
D. 6720
E. 10080

Option “C” is correct.
Required number of ways = ELECTION = 8!/2! = 20160