2D probability question..

in a jar we have 3 balls one red one white one black

3 people choose a ball and return it back.

x represents the number of different colors which the 3 people chose

y represents the number of white balls chosen.

p(x,y)

find p(2,0)

we have in total 27 possibilities

3 people chose 2 different colors(from the existing 3) and non of them was white

so each guy need to chose red or black out of 3 balls

$\displaystyle \binom{3}{1}+\binom{3}{1}$

why the answer is $\displaystyle \frac{2\binom{3}{2}}{27}$