What is the probability that the upturned faces of three fair dice are all of different numbers?

Question

Three fair dice are rolled ($6$ sides). What is the probability that the upturned faces of the three dice are all of different numbers?

I got that the number of possible outcomes total is $6^3$ and the number of possible outcomes for which the upturned dice are all different numbers is $6 * 5 * 4$, so the probability is $\frac{5}{9}$.

Is this correct?

Answer 1

Community wiki answer so the question can be marked as answered:

As Alex remarked: yes, this is correct.