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 $\displaystyle \frac{2\binom{3}{2}}{27}$