7 No Trump
The card game Bridge is played using a standard 52 card deck. At the start of a hand, each player is dealt 13 cards from the deck. One player looks at the 13 cards he was dealt and notices that he has 12 cards in one suit and an ace in a different suit. How many different possible sets of 13 cards could that player have?
Details and assumptions
A standard deck of cards consists of 52 cards, formed by 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King) of 4 suits (clubs, diamonds, hearts and spades)
The answer is 156.
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1 solution
There are 4 suits in the deck, so there are 4 possibilities for which suit the player has 12 cards from. There are then 3 possibilities for which suit the player has the single card in. There are 1 3 choices for which card in the suit of 1 2 is missing. By the rule of product, there are 4 × 3 × 1 3 = 1 5 6 different sets of cards the player could have.