The favorable event $E$ is $\{1, 2, 3, 4, 5, 6\}$ in any order. Also, it is evident that the event of getting one of $\{1, 2, 3, 4, 5, 6\}$ is independent.
On the first roll of the dice, any one of $\{1, 2, 3, 4, 5, 6\}$ can come up with a probability of $1$.
On the second roll, the favorable event is to get any number other than the one got in the first roll. This has a probability of $\frac{5}{6}$.
On the third roll, the favorable event is to get a number other than the one got in the first two rolls. This has a probability of $\frac{4}{6}$.
This continues $\cdots$
The required probability $P(E) = 1 \times \frac{5}{6} \times \frac{4}{6} \times \frac{3}{6} \times \frac{2}{6} \times \frac{1}{6} = 0.0154$