Top 160 Permutation and Combination questions [ 100% FREE ]

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Top 160 Permutation and Combination questions:

81. If the bag contains 3 red balls and 5 green balls, what is the probability of the picking two balls of the same color?
यदि थैले में 3 लाल गेंदें और 5 हरी गेंदें हैं, तो समान रंग की दो गेंदों को चुनने की प्रायिकता क्या है?A. 11/28
B. 13/28
C. 15/28
D. 17/28
E. None of these
Option “B” is correct.Required probability = (3C2 + 5C2 )/ 8C2     = (6 + 20) / 56

= 13/28

82. A box contains 7 black balls, 5 violet balls and 3 yellow balls. If 2 balls are drawn randomly, the probability of getting both the balls is either black or violet balls?
एक बॉक्स में 7 काली गेंदें, 5 बैंगनी गेंदें और 3 पीली गेंदें हैं। यदि 2 गेंदें यादृच्छया निकाली जाती हैं, तो दोनों गेंदों के या तो काले या बैंगनी रंग के होने की क्या प्रायिकता है?A. 22/115
B. 37/121
C. 25/132
D. 31/105
E. None of these
Option “D” is correct.Total probability n(S) = 15C2Required probability n(E) = 7C2 or 5C2

P(E) = n(E)/n(S) = 7C2 or 5C2  / 15C2

= > 31/105

83. A basket contains x black, 4 red and 5 green colour balls. One ball is taken randomly and the probability of getting a green colour ball is 1/3, and then find the number of balls in the basket.
एक टोकरी में x काली, 4 लाल और 5 हरे रंग की गेंदें हैं। एक गेंद यादृच्छया निकाली जाती है और हरे रंग की गेंद मिलने की प्रायिकता 1/3 है, फिर टोकरी में गेंदों की संख्या ज्ञात कीजिए।एक टोकरी में x काली, 4 लाल और 5 हरे रंग की गेंदें हैं। एक गेंद यादृच्छया निकाली जाती है और हरे रंग की गेंद मिलने की प्रायिकता 1/3 है, फिर टोकरी में गेंदों की संख्या ज्ञात कीजिए।A. 12
B. 14
C. 15
D. 18
E. 20
Option “C” is correct.Given,Total no. of probability = 9+x

Required probability = 5/(9+x)=1/3

=>9+x=15=>x=6

84. A bag contains 4 red balls and 3 green balls. If two balls are drawn at randomly, then what is the probability of that balls are red?
एक बैग में 4 लाल गेंदें और 3 हरी गेंदें हैं। यदि दो गेंदों को यादृच्छया निकाला जाता है, तो उन गेंदों के लाल होने की प्रायिकता क्या है?A. 1/6
B. 2/7
C. 3/8
D. 3/5
E. None of these
Option “B” is correct.Required probability = 4C2/7C2= (4 * 3)/(7 * 6)

= 2/7

85. 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 सफेद, 6 लाल और 4 पीले रंग की गेंदें हैं। यदि टोकरी में से एक गेंद यादृच्छया निकाली जाती है और लाल रंग की गेंद मिलने की प्रायिकता 2/5 है, तो टोकरी में गेंदों की कुल संख्या ज्ञात कीजिए ।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

86. A box contains red and green balls and the total number of balls in the box is 15. If the probability of picking a green ball is 0.4, find the number of red balls from the box.
एक बॉक्स में लाल और हरी गेंदें हैं और बॉक्स में गेंदों की कुल संख्या 15 है। यदि हरी गेंद चुनने की प्रायिकता 0.4 है, तो बॉक्स में लाल गेंदों की संख्या ज्ञात करें।A. 8
B. 7
C. 9
D. 6
E. 12
Option “C” is correct.Total number of balls = 15Number of green balls =x

Number of red balls = 15 – x

xC1 / 15C1 = 0.4

x = 6

Number of red balls = 15 – 6 = 9

87. 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 थैले में (x – 1) लाल गेंदें, 3 नीली गेंदें और 4 हरी गेंदें हैं। यदि एक गेंद यादृच्छया निकाली जाती है और हरी गेंद मिलने की प्रायिकता 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 + 62/5 = 4C1/(x + 6)C1

2/5 = 4/(x + 6)

20 = 2x + 12

2x = 8

x = 4

88. A bag contains 45 balls marked 1 to 45. If one ball is drawn at random, then what is the probability that is marked with a number divisible by 4?
एक बैग में 1 से 45 तक चिह्नित 45 गेंदें हैं। यदि एक गेंद यादृच्छिक रूप से निकाली जाती है, तो गेंद के 4 से विभाज्य संख्या के साथ चिह्नित होने की क्या संभावना है?A. 2
B. 3
C. 1
D. 4
E. None of these
Option “E” is correct.Number of marked balls divisible by 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44= 11

Required probability = 11/45

89. A bag contains 30 balls numbered from 1 to 30. Two balls are selected one by one with replacement at random. What is the probability that the first ball is a prime number and the second ball is a perfect square?
एक बैग में 1 से 30 तक चिह्नित 30 गेंदें हैं। यादृच्छिक रूप से प्रतिस्थापन के साथ दो गेंदों को एक-एक करके चुना जाता है। पहली गेंद एक अभाज्य संख्या है और दूसरी गेंद एक पूर्ण वर्ग है, इसकी क्या प्रायिकता है?A. 1/3
B. 1/6
C. 1/9
D. 1/18
E. 1/24
Option “D” is correct.Total balls = 30 Total prime numbers between 1 to 30 = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 = 10 Total perfect square = 1, 4, 9, 16, 25 = 5Probability of selecting first ball = 10/30 = 1/3

Probability of selecting second ball = 5/30 = 1/6

Therefore, probability = (1/3) * (1/6) = 1/18

90. A bag contains 8 balls out which x red balls and remaining are yellow balls. If two balls are drawn at random and the probability that both are red balls is 5/14, then find the number of yellow balls in the bag?
एक बैग में 8 गेंदें हैं जिनमें से x लाल गेंदें और शेष पीली गेंदें हैं। यदि दो गेंदों को यादृच्छिक रूप से निकाला जाता है और दोनों के लाल होने की प्रायिकता 5/14 है, तो बैग में पीली गेंदों की संख्या ज्ञात कीजिए?A. 1
B. 3
C. 2
D. 4
E. 6
Option “B” is correct.Number of red balls=xNumber of yellow balls=(8 – x)

5/14=xC2/8C2   

5/14=x * (x – 1)/56

20=x2 – x

x2 – x – 20=0

x2 – 5x + 4x – 20=0

x(x – 5) + 4(x – 5)=0

x=-4, 5(negative value neglected)

x=5

number of yellow balls=8 – 5=3