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:

121. A bag contains (x + 2) red balls and x yellow balls. If the probability of drawing a yellow ball is 3/7, then find the total number of balls in the bag?
एक थैले में (x + 2) लाल गेंदें और x पीली गेंदें निहित हैं। यदि एक पीली गेंद को निकालने की संभावना 3/7 है, तो थैले में गेंदों की कुल संख्या को ज्ञात कीजिए?A. 12
B. 14
C. 7
D. 21
E. 28
Option “B” is correct.xC1/(x + 2 + x)C1 = 3/7

6x + 6 = 7x

X = 6

Required total = 8 + 6 = 14

122. 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 + xRequired probability= > 6/(10 + x) = 2/5

= > 10 + x = 15

= > x = 5

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

123. A bag contains (x + 2) blue, 5 green and 3 yellow balls. If two balls are drawn randomly and the probability of getting both being green colour balls is 1/12, then find the total number of balls in the bag?
एक बैग में (x + 2) नीली, 5 हरी और 3 पीली गेंदें हैं। यदि दो गेंदों को यादृच्छया निकाला जाता है और दोनों के हरे रंग की गेंद होने की प्रायिकता 1/12 है, तो बैग में गेंदों की कुल संख्या ज्ञात कीजिए?A. 15 balls
B. 18 balls
C. 17 balls
D. 16 balls
E. None of these
Option “D” is correct.Given,

5C2 / (x + 10)C2 = 1/12

(5 * 4) / [(x + 10) (x + 9)] = 1/12

(x + 10) (x + 9) = 240

x2 + 19x + 90 = 240

x2 + 19x – 150 = 0

(x – 6) (x + 25) = 0

x = 6, -25 (Negative value will be eliminated)

Total number of balls = x + 10 = 16 balls

124. A bag contains (x + 5) red balls, 4 green balls and 3 blue balls. If two balls are drawn at random, then the probability that one ball being red and other being green is 32/105. If two balls are drawn at random from the bag, then what is the probability that balls are blue?
एक बैग में (x + 5) लाल गेंदें, 4 हरी गेंदें और 3 नीली गेंदें हैं। यदि दो गेंदें यादृच्छया निकाली जाती हैं, तो एक गेंद के लाल और दूसरी के हरी होने की प्रायिकता 32/105 है। यदि बैग से यादृच्छिक रूप से दो गेंदें निकाली जाती हैं, तो गेंदों के नीले होने की प्रायिकता क्या है?A. 1/7
B. 2/21
C. 1/35
D. 3/35
E. 2/7
Option “C” is correct.(x + 5) C1 * 4C1/(x + 5 + 4 + 3)C2 = 32/105

105x + 525 = 4 * (x + 12) * (x + 11)

105x + 525 = 4x2 + 44x + 48x + 528

4x2 – 13x + 3 = 0

4x2 – 12x – x + 3 = 0

4x(x – 3) – 1(x – 3) = 0

x = 3

Required probability = 3C2/15C2

= 1/35

125. A bag contains (x – 1) red balls, 3 blue balls and 4 green balls. If one ball is taken out randomly and the probability of getting a green ball is 2/5, find the value of x?
एक बैग में (x – 1) लाल गेंदें, 3 नीली गेंदें और 4 हरी गेंदें होती हैं। यदि एक गेंद को यादृक्षिक बाहर निकाला जाता है और हरी गेंद मिलने की संभावना 2/5 है, तो x का मान ज्ञात कीजिए?A. 4
B. 6
C. 2
D. 3
E. 1
Option “A” is correct.Total number of balls = x – 1 + 4 + 3 = x + 6

2/5 = 4C1/(x + 6)C1

2/5 = 4/(x + 6)

20 = 2x + 12

2x = 8

x = 4

126. A bag contains 4 red balls and x orange balls. If the probability of taking an orange ball is 1/5 more than the probability of taking a red ball, and then find the total number of balls in the bag?
एक बैग में 4 लाल गेंदें और x नारंगी गेंदें हैं। यदि एक नारंगी गेंद लेने की प्रायिकता एक लाल गेंद लेने की प्रायिकता से 1/5 अधिक है, और फिर बैग में गेंदों की कुल संख्या ज्ञात कीजिए?A. 12
B. 10
C. 8
D. 15
E. None of these
Option “B” is correct.xC1/(x + 4)C1 – 4C1/(x + 4)C1 = 1/5

5 * (x – 4) = x + 4

5x – 20 = x + 4

x = 6

Total number of bag = 6 + 4 = 10

127. A bag contains 4 red balls, 5 blue balls and x white balls. One ball is drawn at random from the box and the probability of that ball is white is 2/5. If two balls are drawn at random, then find the probability that they are the same colour balls.
एक बैग में 4 लाल गेंदें, 5 नीली गेंदें और x सफेद गेंदें हैं। बॉक्स से यादृच्छिक रूप से एक गेंद निकाली जाती है और उस गेंद के सफेद होने की प्रायिकता 2/5 है। यदि दो गेंदों को यादृच्छिक रूप से निकाला जाता है, तो संभावना निकालें कि वे एक ही रंग की गेंदें हैं।A. 45/118
B. 19/121
C. 57/112
D. 31/105
E. None of these
Option “D” is correct.Total number of balls = 4+5+x = 9+x

xC1/(9+x)C1= 2/5

5x = (9+x)*2

3x =18

x = 6

Required probability = (5C2+4C2+6C2)/15C2

= 5*4+4*3+6*5/(15*14) = 31/105

128. A bag contains 2 red balls, 4 blue balls and x yellow balls. Two balls are drawn at random from the bag and the probability of that balls being blue is 2/7, then find the value of x?
एक बैग में 2 लाल गेंदें, 4 नीली गेंदें और x पीली गेंदें हैं। बैग से यादृच्छिक रूप से दो गेंदें निकाली जाती हैं और उन गेंदों के नीले होने की प्रायिकता 2/7 है, तो x का मान ज्ञात कीजिए?A. 1
B. 3
C. 2
D. 5
E. None of these
Option “A” is correct.The number of blue balls in the bag = 4

The total number of balls in the bag = 2+4+x = x+6

4C2/(x + 6)C = 2/7

7*((4 * 3)/(2 * 1)) = ((x +6) (x + 5)/(2 * 1))*2

(x + 6) (x + 5) = 42

x2 + 11x – 12 = 0

(x + 12)(x – 1) = 0

x = 1

129. In a class,35% of students offered Maths and 25% offered Biology and 5% offered both. If a student is selected at random, then find the probability that he has offered Maths or Biology only.
एक कक्षा में, 35% छात्रों ने गणित की पेशकश की और 25% ने जीव विज्ञान की पेशकश की और 5% ने दोनों की पेशकश की। यदि एक छात्र को यादृच्छिक रूप से चुना जाता है, तो उसके केवल गणित या जीव विज्ञान की पेशकश करने की संभावना क्या है ।A. 50%
B. 60%
C. 55%
D. 45%
E. Can’t be determined
Option “C” is correct.Let the total number of students be 100,

Maths students = 35

Biology students = 25

Both = 5

Required probability = 35/100 + 25/100 – 5/100=55/100=55%

130. A box contains, 5 Sony, 6 Samsung and 4 SanDisk pen drives. 3 pen drives are drawn at random. What is the probability that they are from different company?
एक बॉक्स में 5 सोनी, 6 सैमसंग और 4 सैनडिस्क पेन ड्राइव हैं। यादृच्छिक रूप से 3 पेन ड्राइव निकाले जाते हैं। क्या संभावना है कि वे अलग-अलग कंपनी से हैं?A. 24/91
B. 27/85
C. 33/67
D. 35/78
E. None of these
Option “A” is correct.Total probability n(S) = 15C3

Required probability n(E) = 5C1 and 6C1 and 4C1

P(E) = n(E)/n(S)

P(E) = 5C1 and 6C1 and 4C1 / 15C3

P(E) = 24/91