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.

We’ve noticed a growing trend of people searching for permutation and combination in Hindi. This highlights the widespread appeal and importance of these mathematical concepts. Moreover, if you are looking to build a strong foundation or just seeking to practice, our permutation and combination pdf will surely be of great help. Within it, you’ll find Permutation and Combination problems, and don’t worry – we’ve also got you covered with permutation and combination solutions.

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:

151. A box contains 18 balls marked 1 to 18. If two balls are drawn at random, then what is the probability that is marked with prime number?
एक बॉक्स में 1 से 18 तक चिह्नित 18 गेंदें निहित हैं। यदि दो गेंदों को यादृच्छिक रूप से निकाला गया है, तो इनके अभाज्य संख्या से चिन्हित होने की क्या संभावना है?A. 1/17
B. 7/51
C. 4/51
D. 5/51
E. None of these
Option “B” is correct.Number of marked balls in prime number = 2, 3, 5, 7, 11, 13, 17

Required probability= 7C2/18C2

= (7 * 6)/(18 * 17)

= 7/51

152. A basket contains x white, 6 red and 4 yellow colour balls. If one ball is taken randomly from the basket and the probability of getting a red colour ball is 2/5, then find the total number of balls in the basket?
एक टोकरी में x सफ़ेद, 6 लाल और 4 पीले रंग के गेंद हैं। यदि एक गेंद को टोकरी से यादृच्छिक रूप से लिया गया है और एक लाल रंग की गेंद को प्राप्त करने की संभावना 2/5 है, फिर टोकरी में गेंदों की कुल संख्या को ज्ञात कीजिये?A. 12
B. 18
C. 16
D. 15
E. None of these
Option “D” is correct.Total number of balls = 10 + x

Required probability

= > 6/(10 + x) = 2/5

= > 10 + x = 15

= > x = 5

Total number of balls in the basket = 10 + 5 = 15 balls

153. 35 women can pluck flowers on a garden for 5 hrs per day. If plucking time is increased by 2 hrs, then what is the number of women to be required?
35 महिलाएं प्रतिदिन 5 घंटे के लिए एक बगीचे में फूल तोड़ सकती हैं। यदि तोड़ने का समय 2 घंटे बढ़ा दिया जाए, तो कितनी महिलाओं की आवश्यकता होगी?A. 20
B. 25
C. 22
D. 28
E. None of these
Option “B” is correct.35 * 5 = x * 7

x = 25

154. A bag contains 15 balls marked 1 to 15. If one ball is drawn at random, then what is the probability that is marked with a number divisibleby 2?
एक बैग में 1 से 15 के बीच अंकित 15 गेंदें होती हैं। यदि एक गेंद यादृच्छिक रूप से निकाली जाती है, तो क्या संभावना हैं की वह 2 से विभाजित होने वाली संख्या से अंकित हैं?A. 3/20
B. 7/10
C. 1/5
D. 1/4
E. None of these
Option “E” is correct.Number of marked balls divisible by 2=2, 4, 6, 8, 10, 12, 14

Required probability=7/15

155. A bag contains 24 balls numbered 1 to 24. If three balls are drawn at random, then what is the probability of that the balls are odd numbers?
एक बैग में 1 से 24 तक अंकित 24 गेंदे है। यदि तीन गेंदों को यादृच्छिक रूप से निकाला जाता है, तो विषम संख्या वाले गेंद को प्राप्त करने की प्रायिकता क्या है?A. 3/46
B. 5/46
C. 2/23
D. 3/23
E. None of these
Option “B” is correct.Odd numbered balls = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23

Required probability = 12C3/24C3  

= 12 * 11 * 10/24 * 23 * 22

= 5/46

156. A bag contains 3 red balls, x black balls and 6 yellow balls. One balls is taken randomly and the probability of that ball is yellow is 1/2. Find the total number of balls in the bag?
एक थैले में 3 लाल गेंदें, x काली गेंदें और 6 पीली गेंदें हैं। एक गेंद को यादृच्छिक रूप से निकाला गया है और उस गेंद के पीले रंग के होने की संभावना 1/2 है। थैले में गेंदों की कुल संख्या को ज्ञात कीजिये?A. 10 balls
B. 12 balls
C. 18 balls
D. 20 balls
E. None of these
Option “B” is correct.1/2 = 6C1 / (9 + x)C1    

9 + x = 12

x = 3

Total balls in the bag = 6 + 3 + 3 = 12 balls

157. A bag contains 36 balls in which 33.33% are black balls and the remaining balls are red and blue balls. When two balls are drawn at random from the bag, the probability of selecting one red and one blue ball is 2/9, then find the number of red balls in the bag, if the number of blue balls in the bag is more than the number of red balls?
एक बैग में 36 गेंदें हैं जिनमें 33.33 प्रतिशत काली गेंदें हैं और शेष गेंदें लाल और नीली गेंदें हैं। जब बैग से यादृच्छिक रूप से दो गेंदें निकाली जाती हैं, एक लाल और एक नीली गेंद के चयन की प्रायिकता 2/9 है, तो बैग में लाल गेंदों की संख्या ज्ञात कीजिए, यदि बैग में नीली गेंदों की संख्या, लाल गेंदों की संख्या से अधिक है?A. 16
B. 14
C. 18
D. 10
E. None of these
Option “D” is correct.The number of black balls=36/3=12

The number of blue balls=x

The number of red balls=24-x

xC1*(24-x)C1/36C2=2/9

x*(24-x)/(18*35)=2/9

x2-24x+140=0

x2-14x-10x+140=0

x(x-14)-10(x-14)=0

x=+14, +10

The number of blue balls in the bag is more than the number of red balls

The number of red balls=10

158. A Bag contains 45 balls and each ball is numbered from 1 to 45. If one ball is selected at random from the bag, then what is the probability that the selected ball number is either prime or perfect square?
एक थैले में 45 गेंदें हैं और प्रत्येक गेंद 1 से 45 तक क्रमांकित है। यदि थैले में से एक गेंद यादृच्छया चुनी जाती है, तो इस बात की क्या प्रायिकता है कि चयनित गेंद संख्या या तो अभाज्य है या पूर्ण वर्ग है?A. 1/3
B. 5/9
C. 4/9
D. 2/9
E. 2/3
Option “C” is correct.Prime numbered ball = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

Square number = 1, 4, 9, 16, 25, 36

Required probability = 14/45 + 6/45

= 20/45

= 4/9

159. A bag contains 5 black balls, 7 green and some pink ball. If the probability of choosing a pink ball is 2/3, then, find the total number of balls in the bag?
एक थैले में 5 काली गेंदें, 7 हरी और कुछ गुलाबी गेंदें हैं। यदि गुलाबी गेंद चुनने की प्रायिकता 2/3 है, तो थैले में गेंदों की कुल संख्या ज्ञात कीजिए?A. 33
B. 40
C. 36
D. 44
E. None of these
Option “C” is correct.Let the number of pink ball = x

x/(5+7+x) =2/3

x/(12+x) = 2/3

3x = 24 +2x

x = 24

Total number of balls = 5+7+24 = 36

160. A bag contains 6 blue balls, 4 red balls and x green balls. If the probability of selecting 1 red ball and 1 green ball is 4/33, find the total number of balls in the bag, if x is less than 5.
एक बैग में 6 नीली गेंदें, 4 लाल गेंदें और x हरी गेंदें हैं। यदि 1 लाल गेंद और 1 हरी गेंद के चयन की प्रायिकता 4/33 है, बैग में गेंदों की कुल संख्या ज्ञात कीजिए, यदि x 5 से कम है।A. 18
B. 15
C. 10
D. 12
E. None of these
Option “D” is correct.4C1 * xC­1/(10 + x)C2 = 4/33

4x/[(10 + x)(9 + x)]/2 = 4/33

8x/(90 + 10x + 9x + x2) = 4/33

2x/(90 + 19x + x2) = 1/33

66x = x2 + 19x + 90

x2 – 47x + 90 = 0

x2 – 45x – 2x + 90 = 0

x(x – 45) – 2(x – 45) = 0

x = 45, 2

Number of green balls = 2

Total number of balls in the bag = 6 + 4 + 2 = 12

 

In the dynamic landscape of mathematical concepts and their applications, Permutation and Combination questions stand out as crucial tools for problem-solving. These aren’t just theoretical constructs; they play a foundational role in various real-world scenarios and examinations. From predicting possible outcomes to deciding on optimal strategies, the depth and breadth of permutations and combinations affect our decisions daily.

When we talk about permutation and combination for CAT, it brings to light the importance these concepts hold in competitive examinations. CAT, being a gateway to premier management institutions in India, evaluates aspirants on their grasp over these principles, underlining their significance. As the competitive environment grows fiercer, mastering Permutation and Combination questions becomes not just an option but a necessity for CAT aspirants.

Similarly, the realm of aptitude tests is incomplete without permutation and combination aptitude questions. These questions challenge an individual’s ability to think logically and solve problems efficiently. Aptitude tests, often the first hurdle in numerous selection processes, emphasize the need to understand and apply the principles of permutations and combinations.

With the rising demand for resources in various languages to cater to a diverse group of learners, there’s an increasing interest in permutation and combination in Hindi. This trend not only underscores the universality of these concepts but also the need for inclusive educational resources. By offering explanations and resources in multiple languages, we can ensure that no aspirant feels left out due to language barriers.

In this digital age, having resources at one’s fingertips is invaluable. That’s where the permutation and combination pdf comes into play. A consolidated document containing Permutation and Combination problems paired with their respective permutation and combination solutions can be an indispensable tool for students and educators alike. A PDF format ensures accessibility across devices, allowing learners to engage with the material at their convenience.

It’s worth noting that Permutation and Combination questions are not just limited to management entrance tests or aptitude examinations. These concepts frequently appear in various government exams like Bank, SSC, and Railways. The omnipresence of these questions in multiple high-stakes exams reinforces their importance.

In wrapping up, it’s essential to realize that the journey of mastering permutations and combinations is a continuous one. As with any mathematical concept, the more you engage with Permutation and Combination questions, the clearer they become. Practice is the key. Whether you’re diving into the permutation and combination pdf for self-study, seeking clarifications in Hindi, gearing up for the CAT, or simply looking to better your understanding of permutation and combination problems and their solutions, remember that every effort brings you one step closer to mastery.

To all our readers, as you explore the fascinating world of permutations and combinations, may you find clarity, confidence, and success. Embrace the challenges, celebrate the eureka moments, and remember: in the world of mathematics, every problem, no matter how complex, has a solution waiting to be discovered.