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Printjmc
counting and probability intermediate
Problem
A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (, , , and ), such that there is exactly one card for any given rank and suit. Two of the suits ( and ) are black and the other two suits ( and ) are red. The deck is randomly arranged. What is the probability that the top two cards are both Aces?
Solution
There are 4 ways to choose the first card to be an Ace, then 3 ways to choose the second card to be another Ace. There are ways to choose any two cards. So the probability is .
Final answer
\dfrac{1}{221}