# Understanding the solution to a probability problem, Laplace Model

As I am currently studying for an exam on probability, I've come across a questions for which I have been unable to understand the solution.

The problem reads as follows: The are $N$ (=amount of white balls) + $M$ (=amount of black balls) balls in a box. One takes $n \le N + M$ balls out of the box. Let the random variable $X$ denote the total number of white balls removed from the box. Find the distribution of $X$.

The solution states: $$P[X = k] = \frac{\binom{N}{k}\binom{M}{n-k}}{\binom{N+M}{n}}\text{.}$$

My problem in understand this solution is: Doesn't the binomial coefficient imply that the elements are distinguishable? How can we make we make sense of - for instance - the denominator if $N + M$ means that there are indeed $N+M$ balls but only two "variations" ($N$ white ones, $M$ black ones)? Why is there no error in counting the elements this way?