Sample space A dice is thrown thrice, $$n(s) = 6 \times 6 \times 6$$.

Favorable events $${\omega ^{{r_1}}} + {\omega ^{{r_2}}} + {\omega ^{{r_3}}} = 0$$

i.e. $$({r_1},{r_2},{r_3})$$ are ordered 3-triples which can take values,

$$\left. {\matrix{ {(1,2,3),} & {(1,5,3),} & {(4,2,3),} & {(4,5,3)} \cr {(1,2,6),} & {(1,5,6),} & {(4,2,6),} & {(4,5,6)} \cr } } \right\}$$

i.e. 8 ordered pairs and each can be arranged in 3! ways = 6

$$\therefore$$ $$n(E) = 8 \times 6$$

$$ \Rightarrow P(E) = {{8 \times 6} \over {6 \times 6 \times 6}} = {2 \over 9}$$