GATE | GATE-CS-2000 | Question 1

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.

So,

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

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

(n-1)/4 >= 2

n>=9

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

This explanation has been contributed by Namita Singh.

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