Middle School Level - Probability If you have 3 boxes and 7 coins fall in randomly, what is the probability that 3 coins fall into the first box?

My theory is that if you put one coin into each box until you have a remainder, by using modulus, you get box%coins = x. And then divide by the number of boxes to get the actual probability box%coins = x/boxes

This gives 1/3 as the probability in the case of 3 boxes and 7 coins. Is this correct?

Also, does it work for any number of boxes and coins?
There are $9 \choose 2$ ways seven coins can fall into three boxes, and $5 \choose 1$ ways for four coins to fall into two boxes, so the probability is
$$
{5\choose1}/{9\choose2}={5\over36}
$$
There are $9 \choose 2$ ways seven coins can fall into three boxes, and $5 \choose 1$ ways for four coins to fall into two boxes, so the probability is
$$
{5\choose1}/{9\choose2}={5\over36}
$$