So we play a lottery with the numbers from 1 to 60, and we draw 5 of these numbers. Can someone please explain why the probability that a certain number x appears in this lottery is
$$PR[x appears] = \frac {\binom {59}{4}}{\binom {60}{5}} = \frac {5}{60} $$
Because this doesn't feel natural or logic to me. I know that the denominator stands for all possible permutations of 5 numbers drawn out of this 60. But why is the numerator that $\binom {59}{4} $ ? Are these all possible permutations were we have already drawn the 5?