Question: Suppose you throw a regular and perfectly fair six-sided die $n$ times ($n\geq6$) to obtain a series of random numbers. What is the probability that the series is not biased at all, i.e., that the frequency of every number in the series is exactly $\frac{1}{6}$?

This question came up when I was thinking about an example to illustrate why 'p-hacking' is bad. But I don't know how to calculate the answer to the question. The only thing I believe to know is that this probability approaches $1$ as $n$ goes towards infinity, by the Law of the Large Numbers.

Answer: 
In this metric space every singleton set is open : $\{x\}=B(x,1)$. Hence, every subset is open which makes every subset is closed. So the closure of a countable set is itself and $\mathbb R $ is not countable.
If $D$ is dense in $(\Bbb R,d)$ it must intersect **every** open ball, i.e. every $\{x\}=B\_d(x,1)$. What can you conclude about how many dense sets we have?