Let $w$ be a complex cube root of unity with $ W \neq 1$. A fair die is thrown three times. If $r_1, r_2\:and \: r_3$ are the numbers obtained on the die, then the probability that $ W^{r_1}+W^{r_2}+W^{r_3}=0$ is

Question

$\begin {array} {1 1} (A)\;\large\frac{1}{18} & \quad (B)\;\large\frac{1}{9} \\ (C)\;\large\frac{2}{9} & \quad (D)\;\large\frac{1}{36} \end {array}$