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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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.

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Top 160 Permutation and Combination questions:

71. A bag contains 5 red and 6 blue balls. If two balls are selected at random, find the probability that the balls are in different color.
एक बैग में 5 लाल और 6 नीली गेंदें होती हैं। यदि दो गेंदों को यादृच्छिक पर चुना जाता है, तो इस संभावना को ढूंढें कि गेंद अलग-अलग रंग में हैं।A. 5/11
B. 1/11
C. 6/11
D. 2/55
E. None of these
Option “C” is correct.Required probability = (5C6C1)/11C2= (5 * 6)/(11 * 10/2) = 6/11

72. A bag contains 3 red balls and 4 green balls. What is the probability of selecting 2 green balls from the bag?
एक थैले में 3 लाल गेंदें और 4 हरी गेंदें हैं। थैले में से 2 हरी गेंदों को चुनने की प्रायिकता क्या है ?A. 1/7
B. 2/7
C. 3/7
D. 4/7
E. None of these
Option “B” is correct.Required probability=4C2/7C2= (4 * 3)/(7 * 6)

=2/7

73. What is the probability of selecting 2 blue balls from a bag containing 4 red balls and 5 blue balls?
4 लाल गेंदों और 5 नीली गेंदों वाले बैग में से 2 नीली गेंदों के चयन की प्रायिकता क्या है?A. 5/18
B. 7/18
C. 1/3
D. 2/9
E. 3/7
Option “A” is correct.Required probability=5C2 / 9C2  = 20/72

= 5/18

74. A bag contains 5 red balls and 7 blue balls. Find the probability to choose 2 balls in the same color.
एक बैग में 5 लाल गेंदें और 7 नीली गेंदें हैं। एक ही रंग की 2 गेंदों को चुनने की प्रायिकता ज्ञात कीजिए।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

75. If the box contains 4 red balls and 3 green balls, what is the probability of picking two balls of the same color?
यदि बॉक्स में 4 लाल गेंदें और 3 हरी गेंदें हैं, तो एक ही रंग की दो गेंदों को चुनने की प्रायिकता क्या है?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

76. What is the probability of selecting 2 red balls from the bag containing 4 yellow balls and 5 red balls?
4 पीली गेंदों और 5 लाल गेंदों वाले बैग में से 2 लाल गेंदों के चयन की प्रायिकता क्या है?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

77. A bag contains 4 red balls, 3 blue balls and 6 green balls. If two balls are drawn at random, then what is the probability that either both are red or both are blue?
एक थैले में 4 लाल गेंदें, 3 नीली गेंदें और 6 हरी गेंदें हैं। यदि दो गेंदें यादृच्छया निकाली जाती हैं, तो या तो दोनों के लाल या दोनों के नीले होने की प्रायिकता क्या है?A. 1/26
B. 1/13
C. 3/26
D. 2/13
E. None of these
Option “C” is correct.Required probability = (4C2 + 3C2 )/13C2= 3/26

78. 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 divisible by 2?
एक थैले में 1 से 15 तक चिह्नित 15 गेंदें हैं। यदि एक गेंद यादृच्छया निकाली जाती है, तो गेंद के 2 से विभाज्य होने की संख्या से चिह्नित होने की प्रायिकता क्या है?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, 14Required probability=7/15

79. If the bag contains 5 red balls and 5 green balls, if 2 balls are drawn randomly, then what is the probability that both are green balls?
यदि थैले में 5 लाल गेंदें और 5 हरी गेंदें हैं, यदि 2 गेंदें यादृच्छया निकाली जाती हैं, तो दोनों के हरी गेंद होने की प्रायिकता क्या है?A. 2/9
B. 1/8
C. 4/5
D. 3/8
E. None of these
Option “A” is correct.Required probability=5C2 /10C2   =5 * 4/10 * 9

=2/9

80. The box has 3 red balls, 4green balls and 2 blue balls. If three balls are drawn at random, what is the probability of drawing exactly 2 green balls?
बॉक्स में 3 लाल गेंदें, 4 हरी गेंदें और 2 नीली गेंदें हैं। यदि यादृच्छिक रूप से तीन गेंदें निकाली जाती हैं, तो ठीक 2 हरी गेंदों के निकलने की प्रायिकता क्या है?A. 3/14
B. 2/7
C. 5/14
D. 3/7
E. None of these
Option “C” is correct.Required probability = (4C2 * 5C1)/9C3= ((4 * 3/1 * 2) * 5)/(9 * 8 * 7/1 * 2 * 3)

= 5/14