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Math Help - Expected number of collisions

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    MJ0
    MJ0 is offline
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    Expected number of collisions

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

    There are m open boxes, each of which can contain at most one ball. There is a ball throwing machine that fires a total of n balls 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, is 1/m (equal for each box). The thrown ball will always fall onto one of the boxes. However, the probability that the ball will actually fall into any box is less than 1 after the first throw (provided that n > 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, given m boxes and n balls.

    Thanks in advance.
    Last edited by MJ0; November 30th 2009 at 07:21 AM.
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