Let omega be a complex cube root unity w...

Let `omega` be a complex cube root unity with `omega != 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 `omega^(r1) + omega^(r2) + omega^(r3)=0` is (a) `1/18` (b) `1/9` (c) `2/9` (d) `1/36`

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