We have one (1) bin with balls. The bin contains twelve balls, three red, four green, and five blue. Alice conducts the following experiment: Alice picks three balls from the bin uniformly at random. What is the probability that Alice picks one red, one green, and one blue ball? That is, what is the probability that Alice picks three balls, one of each color? The probability is the rational number p/q where p is _________________ and q is _____________________

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