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.

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Top 160 Permutation and Combination questions:

111. A bag contains 5 red balls, 4 blue balls and 6 green balls, three balls are drawn at random. Find the probability that at least one ball is in red color.
एक बैग में 5 लाल गेंदें, 4 नीली गेंदें और 6 हरी गेंदें होती हैं, तीन गेंदें यादृच्छिक रूप से निकाली जाती हैं। प्रायिकता ज्ञात करें कि कम से कम एक गेंद लाल है।A. 21/23
B. 47/91
C. 11/67
D. 67/91
E. None of these
Option “D” is correct.Required probability = 1 – none in red color

= 1 – 10C3/15C3

= 1 – [(10 * 9 * 8/(3 * 2))/((15 * 14 * 13)/(3 * 2))]

= 67/91

112. A bag contains 3 red, 2 blue and 4 green balls. 2 balls are drawn randomly from the bag. Find the probability that out of 2 balls at least one ball is blue?
एक बैग में 3 लाल, 2 नीली और 4 हरी गेंदें हैं। बैग से यादृच्छिक रूप से 2 गेंदें निकाली जाती हैं। 2 गेंदों में से कम से कम एक गेंद नीली होने की प्रायिकता ज्ञात कीजिए?A. 5/36
B. 5/12
C. 1/2
D. 7/12
E. None of these
Option “B” is correct.Required probability = 7C1 * 2C1/9C2 + 2C2/9C2 

= (14 + 1)/36

= 15/36

= 5/12

113. A box contains 12 oranges, 8 apples and a certain number of bananas and the average number of fruits in the box are 9. 3 fruits are drawn at random, then find the probability that at least 1 orange and at least 1 banana is drawn.
एक बॉक्स में 12 संतरे, 8 सेब और एक निश्चित संख्या में केले हैं और बॉक्स में फलों की औसत संख्या 9 है। 3 फल यादृच्छिक रूप से निकाले जाते हैं, तो कम से कम 1 संतरा और कम से कम 1 केला निकाले जाने की प्रायिकता ज्ञात कीजिए।A. 61/30
B. 158/325
C. 155/321
D. 154/325
E. None of these
Option “D” is correct.Total number of fruits in the box = 9 * 3 = 27

Number of bananas = 27 – 12 – 8 = 7

Required probability = ((12C1 * 8C1 * 7C1) + (12C2 * 7C1) + (12C1 * 7C2))/27C3

= ((12 * 8 * 7) + (6 * 11 * 7) + (12 * 7 * 3))/2925 = 1386/2925 = 154/325

114. A box contains 20 milk chocolates, 10 dark chocolates and 20 white chocolates. If two chocolates are drawn at random from the box, then find the probability of selecting at least one of them is milk chocolates?
एक बॉक्स में 20 मिल्क चॉकलेट, 10 डार्क चॉकलेट और 20 व्हाइट चॉकलेट हैं। यदि बॉक्स में से यादृच्छिक रूप से दो चॉकलेट निकाली जाती हैं, तो उनमें से कम से कम एक मिल्क चॉकलेट के चयन की प्रायिकता ज्ञात कीजिए?A. 99/196
B. 108/343
C. 143/490
D. 158/245
E. None of these
Option “D” is correct.

The total number of chocolates in the box = 20 + 10 + 20 = 50

Total number of milk chocolates = 20

Total number of chocolates which are not milk chocolates = 30

Required probability = (20C1 * 30C1 + 20C2)/50C2

= (20 * 30 + 10 * 19)/(25 * 49) = (600 + 190)/1225 = 790/1225 = 158/245

115. A box contains 3 apples and 2 Oranges. If two fruits are picked at random, then what is the probability that is at least one apple in the drawn fruits?
एक बॉक्स में 3 सेब और 2 संतरे होते हैं। यदि दो फलों को यादृच्छिक रूप से उठाया जाता है, तो क्या संभावना है कि उठाये गए फलों में कम से कम एक सेब है?A. 9/10
B. 4/5
C. 7/10
D. 3/5
E. None of these
Option “A” is correct.Required probability = (3C1 * 2C1 + 3C2)/5C2

= [(3 * 2) + 3]/(5 * 2)

= 9/10

116. A box contains 3 Black pens, 5 Blue pens and 4 Red pens. 4 pens are drawn randomly, then what is the probability that the pens contain at least 2 black pens?
एक बॉक्स में 3 काले पेन, 5 नीले पेन और 4 लाल पेन हैं। 4 पेन यादृच्छया निकाले जाते हैं, तो इसकी क्या प्रायिकता (संभावना) है कि पेन में कम से कम 2 काले पेन हों ?A. 23/55
B. 13/55
C. 27/55
D. 39/55
E. None of these
Option “B” is correct.Required probability = (2 black and 2 other pen) or (3 black and 1 other pen)

= [(3C2*9C2) + (3C3*9C1 ) ] / 12C4

= [(3*2/2)*(9*8/2) + (1*9)] /495

= [(3*36) +9] /495

= (108 +9)/495 = 117/495=13/55

117.  A bag contains 5 white balls, 3 black balls and 4 red balls. If three balls are picked at random, find the probability that it contains at most 2 white balls.
एक बैग में 5 सफेद गेंदें, 3 काली गेंदें और 4 लाल गेंदें हैं। यदि यादृच्छिक रूप से तीन गेंदें चुनी जाती हैं, तो इसकी प्रायिकता ज्ञात कीजिए कि इसमें अधिकतम 2 गेंदें सफेद हों।A. 11/13
B. 15/17
C. 10/19
D. 21/22
E. None of these
Option “D” is correct.Total number of balls in the bag = 5 + 3+ 4 = 12

Required probability = (5C2 * 7C1 + 5C* 7C2 + 7C3)/12C3 = (5 * 2 * 7 + 5 * 7 * 3 + 7 * 5)/(4 * 11 * 5) = (70 + 105 + 35)/(4 * 11 * 5)

= 210/220 = 21/22

118. From a group of 8men and 4women, 6persons are to be selected to form a committee,so that at most 3 men are there in the committee, in how many ways it can be done?
8 पुरुषों और 4 महिलाओं के समूह से, 6 व्यक्तियों को एक समिति बनाने के लिए चुना जाना है, ताकि कम से कम 3 पुरुष समिति में हों, कितने तरीकों से यह किया जा सकता है?A. 236
B. 248
C. 252
D. 270
E. None of these
Option “C” is correct.
119. What is the probability of selecting the committee of 5 members from the group of 7men and 6women, the committee should have at most 2 women?
7 पुरुषों और 6 महिलाओं के समूह में से 5 सदस्यों की समिति को चयनित करने की संभावना क्या है, समिति में अधिकतम 2 महिलाएं होनी चाहिए?A. 48/143
B. 28/134
C. 32/143
D. 84/143
E. None of the above
Option “D” is correct.
120. In how many ways a selection of 4 balls that has at least 2 red balls can selected from 4 red balls and 5 pink balls?
4 लाल गेंद और 5 गुलाबी गेंद से 4 गेंदों का चयन कितने तरीकों से किया जा सकता है जिसमें कम से कम 2 लाल गेंदें होती हैं?A. 60
B. 80
C. 100
D. 50
E. None of these
Option “E” is correct.Number of ways = 4C+ 5C2 * 4C2 + 5C1 * 4C= 10 * 6 + 5 * 4 + 1

= 60 + 20 + 1 = 81