12 Balls

You have the following collection of brightly colored balls:

You put them all in a bag, mix them up and them pick them out (without replacement) one by one.

If the probability that the first three you pick will be the same color, the second three will be the same color and the third three you pick will be the same color, is $$\frac{1}{a}$$ then what is $$a$$?

×