Forty slips are placed into a hat, each bearing a number $1,2,\dots ,8$, with each number entered on five slips. Four slips are drawn from the hat at random and without replacement. Let $p$ be the probability that two of the slips bear a number $a$ and the other two bear a number $b\ne a$. Let $q$ be the probability that three of the slips bear a number $c$ and the remaining slip bears a number $d\ne c$. What is the value of $\frac{q}{p}$?