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:

141. 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 blue?
एक बैग में 4 लाल गेंदें, 3 नीली गेंदें और 6 हरी गेंदें होती हैं। यदि दो गेंदों को यादृच्छिक रूप से खींचा जाता है, तो क्या संभावना है कि दोनों लाल हैं या दोनों नीले हैं?A. 1/26
B. 1/13
C. 2/13
D. 3/26
E. None of these
Option “D” is correct.Required probability = (4C2 + 3C2)/13C2

= 3/26

142. A bag contains 2 red balls, 4 blue balls and 6 green balls, If two balls are drawn at random, then find the probability that they are either in blue or green colour.
एक बैग में 2 लाल गेंदें, 4 नीली गेंदें और 6 हरी गेंदें हैं, यदि दो गेंदें यादृच्छया निकाली जाती हैं, तो उनके या तो नीले या हरे रंग की होने की प्रायिकता ज्ञात कीजिए।A. 5/21
B. 1/132
C. 9/22
D. 5/22
E. None of these
Option “E” is correct.Required probability = (4C2 + 6C2) / (12C2) = [(4 * 3) + (6 * 5)] / (12 * 11)

= 7/22

143. A bag contains 3 red balls, 5 blue balls and 6 green balls. Two balls drawn at random, what is the probability that the balls are either red or green balls?
एक थैले में 3 लाल गेंदें, 5 नीली गेंदें और 6 हरी गेंदें हैं। दो गेंदों को यादृच्छिक रूप से निकाला गया है, गेंदों के या तो लाल या हरी होने की क्या संभावना है?A. 8/91
B. 18/91
C. 6/91
D. 5/91
E. None of these
Option “B” is correct.Probability = (3C6C2) / 14C2

= [3 + (6 * 5)/2] / [(14 * 13/2)] = 18/91

144. A bag contains 3 Red, 4 Green and 5 Blue balls. If two balls are drawn at random, then what is the probability that balls are either Red or Blue?
एक बैग में 3 लाल, 4 हरा और 5 नीला गेंद हैं। यदि दो गेंदों को यादृच्छिक रूप से निकाला जाता है, तो क्या प्रायिकता है कि गेंदें लाल या नीली हैं?A. 13/55
B. 12/55
C. 13/66
D. 17/66
E. 5/22
Option “C” is correct.Required probability = (3C2 + 5C2)/12C2   

= 13/66

145. A bag contains 3 red, 5 blue and 6 black balls. If two balls are drawn at random, then what is the probability of that balls either both are red or both blue?
एक थैले में 3 लाल, 5 नीली और 6 काली गेंदें निहित हैं। यदि दो गेंदों को यादृच्छिक रूप से निकाला गया है, तो क्या संभावना है कि गेंदें या तो दोनों लाल या दोनों नीली हैं?A. 1/5
B. 2/7
C. 3/5
D. 1/7
E. 3/4
Option “D” is correct.Required probability = (3C2 + 5C2)/14C2

=13 / (7*13)

= 1/7

146. A Bag contains 38 balls and each ball is numbered from 4 to 41. If one ball is selected at random from the bag, then what is the probability of that selected ball number is either prime or perfect cube?
एक बैग में 38 गेंदें होती हैं और प्रत्येक गेंद 4 से 41 तक होती है। यदि एक गेंद को बैग से यादृच्छिक पर चुना जाता है, फिर उस चयनित गेंद नंबर की संभावना क्या है या तो अभाज्य या पूर्णघन है?A. 6/19
B. 11/38
C. 7/19
D. 13/38
E. 5/19
Option “D” is correct.Prime numbered ball = 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41

Perfect cube = 8, 27

Required probability = 11/38 + 2/38

= 13/38

147. In a box, there are 5 English books, 10 Hindi books and 15 Tamil books. One book is picked up randomly. What is the probability that it is neither English book nor Tamil book?
एक बॉक्स में 5 अंग्रेजी किताबें, 10 हिंदी किताबें और 15 तमिल किताबें हैं। एक किताब अनियमित रूप से निकाली गई है। क्या प्रायिकता है कि यह न तो अंग्रेजी किताब है और न ही तमिल किताब है?A. 3: 1
B. 1: 3
C. 1: 2
D. 2: 1
E. None of these
Option “B” is correct.
Required probability = 10/(5 + 10 + 15) = 10/30 = 1/3
148. One ball is picked up randomly from a bag containing 11 red, 8 black and 13 blue balls. What is the probability that it is neither red nor blue?
एक गेंद को 11 लाल, 8 काली और 13 नीली गेंदों वाले बैग से यादृक्षिक निकाला जाता है। क्या प्रायिकता है कि यह न तो लाल है और न ही नीला है?A. 2/5
B. 1/4
C. 3/5
D. 1/3
E. None of these
Option “B” is correct.Total number of balls = 11 + 8 + 13 = 32

Let, E be the event where the ball can be selected which is neither red nor blue.

Therefore, P(E) = 8/32 = 1/4.

149. One card is drawn at random, what is the probability if the card is neither a club nor a jack?
एक कार्ड यादृच्छिक रूप से निकाला जाता है, कार्ड के न तो चिड़ी और न ही गुलाम होने की क्या संभावना है?A. 11/13
B. 10/13
C. 9/13
D. 8/13
E. 12/13
Option “C” is correct.Total cards = 52

Total club = 13

Total jack = 4

Required probability = 1 – (13/52 + 3/52)

= 9/13

150. The box has 3 red balls and 4 yellow balls. If a ball takes randomly, then what is the probability that either red or yellow?
बॉक्स में 3 लाल गेंदें और 4 पीली गेंदें हैं। यदि किसी गेंद को यादृच्छिक रूप से लेते है, तो क्या संभावना है कि गेंद या तो लाल या पीली है?A. 1/2
B. 1
C. 2/3
D. 3/4
E. None of these
Option “B” is correct.
Required probability = 3C1 + 4C1/7C1 = 1