question_answer

Let \[\omega \] be a complex cube root of unity with\[\omega \ne 1.\] A fair die is thrown three times.  If \[{{n}_{1}},\]\[{{n}_{2}}\] and \[{{n}_{3}}\] are the numbers obtained on the die, then the probability that \[{{\omega }^{{{n}_{1}}}}+{{\omega }^{{{n}_{2}}}}+{{\omega }^{{{n}_{3}}}}=0\] is ________.

A)  \[\frac{2}{9}\] 

B)  \[\frac{1}{9}\]

C)  \[\frac{1}{18}\]                        

D)  \[\frac{1}{36}\]

E)  None of these