The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are ...

Question

The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from the same suit is

A. 3   B. 8   C. 9   D. 12

Accepted Answer

Minimum 9 cards must be dealt to guarantee three from the same suit. A standard deck has 52 cards in 4 suits (spades, hearts, diamonds, clubs), 13 cards each. We want to guarantee that no matter how the cards come out, at least 3 are from the same suit. The adversarial worst case is drawing as many cards as possible without any suit reaching 3 — that means drawing 2 from each of the 4 suits = 8 cards. The very next card, the 9th, must make some suit reach 3.