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

Let \[\omega \] be a complex cube root of unity with \[\omega \ne 1.\]

1.	Let \[\omega \] be a complex cube root of unity with \[\omega \ne 1.\] A fair die is thrown three times. If \[r,{{r}_{2}}\] and \[{{r}_{3}}\] are the numbers obtained on the die, then the probability that \[{{\omega }^{{{r}_{1}}}}+{{\omega }^{{{r}_{2}}}}+{{\omega }^{{{r}_{3}}}}=0\] is
A.	43101
B.	44440
C.	44441
D.	13150
Answer» D. 13150

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

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