In these lecture notes (http://cgarrod.org/Book/chapter%201.pdf), they explain how to compute the probability of finding $n$ indistinguishable particles in volume $v$, given that there are $N$ particles and the total volume is $V$. The formula is: $$ P[\text{$n$ particles in $V$}] = \binom{N}{n} p^n (1-p)^{N-n} $$ where $p$ is $$ p = \frac{v}{V} $$
I would like to know how this formula generalizes if one wants to compute "the probability of finding $n_1$ particles in volume $v_1$ and $n_2$ particles in volume $v_2$, given that there are $N$ indistinguishable particles in total, that the total volume is $V$ and that $v_1$ and $v_2$ are disjoint."