Eighteen slips are placed into a hat, each bearing a number $1,2,\dots ,6$, with each number entered on three slips. Three slips are drawn from the hat at random and without replacement. Let $p$ be the probability that all three slips bear the same number. Let $q$ be the probability that two of the slips bear a number $a$ and the other slip bears a number $b\ne a$. What is the value of $\frac{q}{p}$?