Each of the 20 balls is tossed independently and at random into one of the 5 bins. Let $p$ be the probability that some bin ends up with 3 balls, another with 5 balls, and the other three with 4 balls each. Let $q$ be the probability that every bin ends up with 4 balls. What is $\frac{p}{q}$ ? 
选项为:A:$$1$$  B:$$4$$  C:$$8$$  D:$$12$$  E:$$16$$  请回答其中一个选项.