I have had a hard time trying to solve the following problem. I would be pleased if anyone can help me on this:

There aremopen boxes, each of which can contain at most one ball. There is a ball throwing machine that fires a total ofnballs towards the boxes, one by one. For each box, the probability that when the machine throws a ball, the ball falls onto that specific box, is1/m(equal for each box). The thrown ball will always fall onto one of the boxes. However, the probability that the ball will actually fallintoany box is less than 1 after the first throw (provided thatn> 1), because a box which is already filled with a ball (from the previous throw(s)), will prevent the thrown ball from falling into that box. Call this a collision. Assume that a thrown ball, which collides with one of the balls in a box, simply disappears.

I need a formula with which I can calculate the expected number of collisions, givenmboxes andnballs.

Thanks in advance.