GATE 2000 CS question 1.1 (Probability)

1.1. The mininum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards, to guarantee that three cards are from some same suite is:
(a) 3 (b) 8 (c) 9 (d) 12

Explanation (answer at the end):

This is a standard cards problem, and the solution is quite easy. First of all, there are 4 suites in a deck of cards (usually called Spades, Clubs, Hearts and Diamonds, though several other names also have been given to them). Each suite has 13 cards in it.

We want a guarantee that three cards from the same suite come to us, we shall assume the worst case and ensure 3 cards of same suite occur even in that case.

The worst case here is that, as we pick cards, each card is of a different type. In that case, with the first 4 picks, we'd have taken one card of each suite. With the next 4 cards, we'd have 2 cards of each suite. Now, if we pick another card, whatever suite it may be, we have 2 other cards of that suite already. So, we now have 3 cards of the same suite, which was our objective!!

So, from the above, it's clear that to guarantee that three cards are from some same suite, we have to pick 9 cards from the deck.

Answer: (c)