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GATE | GATE-CS-2000 | Question 1

  • Difficulty Level : Expert
  • Last Updated : 28 Jun, 2021
Geek Week

The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is
(A) 3
(B) 8
(C) 9
(D) 12

Answer: (C)

Explanation: Total number of suits is 4

We need minimum 9 cards to make sure that there are 3 cards of same suit.

For example, With 8 cards, we can have 2 cards of each suit.

This problem can even be solved using the pigeon hole principle.

Applying pigeon hole principle to the given problem:

pigeons means 4 hole represent 4 suites
and n pigeons be number of cards to be drawn.


floor [(n-1)/p] +1=3

floor[(n-1)/4] =2

(n-1)/4 >= 2


minimum 9 cards must be picked
Hence, the correct must be 9

This explanation has been contributed by Namita Singh.

Quiz of this Question

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