Question

How many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same suit are chosen?

Answer 1

Imagine we have no more 2 cards of each suit. This means that we have no more than 2*4 = 8 cards at all.

Therefore, by selecting the 9th card, by the pigeon principle(9 cards and 4 suits), we will guarantee at least 3 cards of the same suit will be chosen.

Along with that, this number can't be less than 9, since we have provided with the example for 8 cards.

So, the least answer is 9.