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Let \( \omega \) be a complex cube root of unity with \( \omega \neq 1 \). A fair dice is thrown three times. If \( \mathrm{r}_{1}, \mathrm{r}_{2} \) and \( \mathrm{r}_{3} \) are the
\( \mathrm{P} \) numbers obtained on the dice, then the probability that \( \omega^{\mathrm{r}_{1}}+\omega^{\mathrm{r}_{2}}+\omega^{\mathrm{r}_{3}}=0 \) is

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(A) \( \frac{1}{18} \)
(B) \( \frac{1}{9} \)
(C) \( \frac{2}{9} \)
(D) \( \frac{1}{36} \)
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