In two decks of cards, what is the least amount of cards you must take to be guaranteed at least one four-of-a-kind?
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13
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4
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536
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40
To guarantee a four-of-a-kind, you must consider the worst-case scenario. You could pick 3 of every rank (13 ranks * 3 = 39 cards). The 40th card must complete a set of four.
To answer this question, let's consider the worst-case scenario in which you have the least amount of cards to guarantee at least one four-of-a-kind.
In a standard deck of 52 playing cards, there are 13 ranks (Ace, 2, 3, ..., 10, Jack, Queen, King) and 4 suits (Hearts, Diamonds, Clubs, Spades). To guarantee at least one four-of-a-kind, you would need to have all four cards of each rank.
Since there are 13 ranks, you would need 4 cards for each rank, resulting in a total of 13 x 4 = 52 cards. Therefore, you would need to take at least 52 cards to be guaranteed at least one four-of-a-kind.
However, the question states that you have two decks of cards. Therefore, you would need to double the number of cards to have all four cards of each rank from both decks.
Hence, the correct answer is D) 40, as you would need to take at least 40 cards from the two decks to be guaranteed at least one four-of-a-kind.