Suppose we have $M$ balls placed randomly into $N$ boxes, wherein each ball has an equal chance of landing in each bin. How would we go about finding the expected number of balls in the first box?
I assumed we could use a binomial distribution, wherein we would regard a ball being thrown into the first box as a success, and the probability of success is $1/N$. Hence, from this, the expected value of balls in the first box is $M/N$. Is this a correct approach?