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Omni-MATH / Wayne has 3 green buckets, 3 red buckets, 3 blue buckets, and 3 yellow buckets.…

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problem

Wayne has 3 green buckets, 3 red buckets, 3 blue buckets, and 3 yellow buckets. He randomly distributes 4 hockey pucks among the green buckets, with each puck equally likely to be put in each bucket. Similarly, he distributes 3 pucks among the red buckets, 2 pucks among the blue buckets, and 1 puck among the yellow buckets. What is the probability that a green bucket contains more pucks than each of the other 11 buckets?

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