Question

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 1

The correct option is C 9

Let the number of cards to be dealt from an arbitratily shuffled deck of 52 cards be n.
Number of suits = 4
Required number of cards from the same suit = 3.
So by pigeonhole principle

$\lfloor \frac{n-1}{4}\rfloor +1=3$

$\lfloor \frac{n-1}{4}\rfloor =2$

$\lfloor n-1\rfloor =8$
$n\ge 9$

So 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 9.