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:

91. A hand of playing cards contain the following 10 cards: 3 cards of Hearts, 2 cards of Spades, 3 cards of Clubs and 2 cards of Diamonds. If 2 cards are randomly dealt from the hand, what is the probability that both are black coloured cards?

ताश के एक पैकेट में निम्नलिखित 10 कार्ड हैं: हर्ट्स के 3 कार्ड, हुकुम के 2 कार्ड, क्लब के 3 कार्ड और डायमंड के 2 कार्ड। यदि 2 कार्डों को पैकेट से यादृच्छिक रूप से बांटे जाते हैं, तो क्या संभावना है कि दोनों काले रंग के कार्ड हैं?A. 4/9
B. 2/9
C. 3/8
D. 5/8
E. 4/11

Option “B” is correct.

Black coloured cards = 3 + 2 = 5

Probability = (5C2)/(10C2) = 2/9

92. 2 cards are drawn from a pack of 52 cards. Find the probability of picking 2 red cards.
52 ताश के पत्तों के एक पैकेट से 2 पत्ते निकाले जाते हैं। 2 लाल पत्ते लेने की प्रायिकता ज्ञात कीजिए।A. 14/91
B. 25/51
C. 25/102
D. 3/4
E. None of these
Option “C” is correct.
Required probability = 26C2/52C2 = (26 * 25)/(52 * 51) = 25/102
93. 3 cards are drawn from a well shuffled pack of 52 cards. Find the probability that there are 2 jack and 1 queen or all 3 are black.

52 ताश के पत्तों के एक अच्छी तरह से फेंटे गए पैक से 3 पत्ते निकाले जाते हैं। 2 गुलाम और 1 रानी या सभी 3 काले होने की प्रायिकता ज्ञात कीजिए।A. 656/5525
B. 554/5525
C. 656/1525
D. 554/1525
E. None of these

Option “A” is correct.
94. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is?

एक कार्ड, 52 कार्डों के पैक से निकला जाता है। चिड़ी की बेगम या पान का बादशाह निकालने की संभावना क्या है?A. 1/26
B. 2/25
C. 3/26
D. 4/25
E. 7/26

Option “A” is correct.

Here, n(S) = 52

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2

P(E) =n(E)/n(S)=2/52=1/26

95. Four cards are drawn from the pack of 52 cards. What is the probability that it has two aces and 2 king cards?

52 ताश के पत्तों के पैक से चार पत्ते निकाले जाते हैं। इसकी क्या प्रायिकता है कि इसमें दो इक्के और 2 बादशाह पत्ते हों?A. 35/270725
B. 36/270725
C. 32/270725
D. 22/270725
E. None of these

Option “B” is correct.

Number of Ace cards = 4

Number of King cards = 4

Required possibility = (4C2*4C2)/ 52C4

= [(4*3/2)*(4*3/2)]/(52*51*50*49/4*3*2) = 36/270725

96. If two cards are drawn at random from a pack of cards, then what is the probability of that both the cards are either queens or Kings?

यदि कार्ड के एक पैकेट से दो कार्ड यादृच्छिक रूप से निकाले जाते हैं, तो इस बात की क्या संभावना है कि दोनों कार्ड या तो रानी या राजा हैं?A. 1/221
B. 2/221
C. 3/221
D. 4/221
E. 5/221

Option “B” is correct.

Required probability = 4C2/52C2 + 4C2/52C2 

= 2/221

97. If two cards are drawn from the pack at random, then what is the probability of that cards are king?

यदि ताश की गड्डी से दो ताश के पत्तों को यादृच्छिक रूप से निकाला जाता है, तो उन ताश के पत्तों के राजा होने की संभावना क्या है?A. 1/221
B. 2/221
C. 3/221
D. 4/221
E. None of these

Option “A” is correct.

Required probability = 4C2/52C2

= 4 * 3/52 * 51

= 1/221

98. One card is drawn at random from a pack of cards. What is the probability, if the card is neither King nor queen?

कार्ड के एक पैकेट से एक कार्ड यादृच्छिक रूप से खींचा जाता है। क्या संभावना है, अगर कार्ड न तो राजा और न ही रानी है?A. 11/13
B. 9/13
C. 7/13
D. 10/13
E. None of these

Option “A” is correct.

Number of King = 4

Number of queen = 4

Required probability = 1 – (4/52 + 4/52)

= 1 – (2/13)

= 11/13

99. Two cards are drawn at the random from a pack of cards. What is the probability that both are Kings?

ताश के पत्तों के एक पैकेट से यादृच्छिक रूप से दो पत्ते निकाले जाते हैं। दोनों के राजा(किंग) होने की प्रायिकता क्या है?A. 3/221
B. 4/221
C. 5/221
D. 1/221
E. None of these

Option “D” is correct.

The number of kings in the pack=4

Total number of cards=52

Required probability=4C2 /52C2 = (4 * 3)/(52 * 51)

=1/221

100. One card is drawn at random from the cards. What is the probability, if the card is neither jack nor King?

कार्डों में से एक कार्ड यादृच्छया निकाला जाता है। यदि कार्ड न तो जैक और न ही किंग है, तो इसकी क्या प्रायिकता है?A. 11/13
B. 10/13
C. 12/13
D. 9/13
E. None of these

Option “A” is correct.

Total number of cards = 52

Number of jack = 4

Number of King = 4

Required probability = 1 – (4/52 + 4/52)

= 44/52

= 11/13