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. Once he is finished, what is the probability that a green bucket contains more pucks than each of the other 11 buckets?
Answer Choices
A. \dfrac{97}{243}
B. \dfrac{89}{243}
C. \dfrac{93}{243}
D. \dfrac{95}{243}
E. \dfrac{91}{243}