600 identical balls are distributed randomly in 6 numbered boxes (all balls are to be distributed and boxes can be empty). What is the probability that exactly 300 balls will end up in the first 3 boxes?

When there are $n$ identical objects to be distributed among r distinct bins, we will have $\left(r-1\right)$ bars that divide them into $r$ distinct groups. The total objects that will be distributed are $\left(n+r-1\right)$, and $\left(r-1\right)$ of these distributions are made for the bars alone. Thus, there are $\left(\stackrel{n+r-1}{r-1}\right)$ possible placements of the bars.

Equivalently, there are $\left(\stackrel{n+r-1}{r-1}\right)$ possible distributions of n identical objects among r distinct bins.