Question 10
There are $18$ cards. Each card is labelled with exactly one positive integer from $\{1,2,3,4,5,6,7,8,9\}$, with exactly two cards of each label. Amy randomly selects two cards at the same time and tells Brandon only the product of their numbers. Brandon wins if he can determine the two numbers in one try without guessing. What is the probability $\frac{q}{p}$, where $p,q$ are relatively prime, that Brandon wins?