Solution (source code)

= Solution

Choose the first face in six ways, the second in five ways avoiding the first, and the third in four ways avoiding both. Thus
$$
\boxed{P(D)=\frac{6\cdot5\cdot4}{216}=\frac59.}
$$
Each ordered outcome is equally likely in this <sample space>, so dividing the count by $216$ gives the <probability>.