SOLUTION: How many cards must be drawn (without replacement) from a standard deck of 52 to guarantee that twelve of the cards will be of the same suit.

Question 856100: How many cards must be drawn (without replacement) from a standard deck of 52 to guarantee that twelve of the cards will be of the same suit.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
there are 4 suits in the deck.
there are 13 cards in each suit for a total of 52 cards in the deck.
the suits are clubs spades, diamonds, and hearts.

it's possible to get 4 * 11 = 44 cards out of the deck and still not be guaranteed that 12 of those cards will be of the same suit, because you could get 11 of clubs + 11 of spades + 11 of diamonds + 11 of hearts.

however, when you draw the 45th card out of the deck, it will have to belong to one of those suits, so the answer appears to be that you have to draw 45 times to be guaranteed that 12 of the cards will be of the same suit.

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