Ball Probability

In a bag, there are 12 balls, with three balls colored blue, three colored red, three colored yellow, and three colored black. I draw 4 balls in succession without replacement. The probability that the first is not blue, the second is not red, the third is not yellow, the fourth is not black and all four balls are different-colored can be expressed as \(\dfrac{p}{q}\) for positive coprime integers \(p\) and \(q\). Find \(p+q\).

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