A standard die is a cube whose faces are labelled 1, 2, 3, 4, 5, 6. Raffi rolls a standard die three times obtaining the results $p, q$ and $r$ on the first, second and third rolls, respectively. What is the probability that $p<q<r$ ?
The numbers $p, q$ and $r$ must be three different numbers from the list 1, 2, 3, 4, 5, 6 .

There are $\binom{6}{3}=20$ ways of choosing 3 numbers from 6 .

Once these numbers are chosen, there is only one way to assign them to $p, q$ and $r$ since $p<q<r$.

Each time a standard die is rolled, there are 6 equally likely results, so when the die is rolled 3 times, there are $6^{3}=216$ equally likely combinations that can occur.

Therefore, the probability of success (that is, of rolling three numbers in increasing order) is $\frac{20}{216}$ or $\frac{5}{54}$.

ANSWER: $\frac{5}{54}$