A pinochle deck has forty-eight cards, two of each of six denominations (9, J, Q, K, 10,

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A pinochle deck has forty-eight cards, two of each of six denominations (9, J, Q, K, 10, A) and the usual four suits. Among the many hands that count for meld is a roundhouse, which occurs when a player has a king and queen of each suit. In a hand of twelve cards, what is the probability of getting a “bare” roundhouse (a king and queen of each suit and no other kings or queens)?

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