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3 identical objects are randomly thrown into 5 similar boxes, what is the probability that at least one box has more than 2 objects. If I am not wrong, this is the case of indistinguishable objects and indistinguishable boxes. My work is the following:

$$P(X=2) = (1/5)^2 (4/5)$$ $$P(X=3) = (1/5)^3$$

I omitted the use of combinations because all the boxes are identical. However, the addition of the two probabilities isn't the correct answer. I would appreciate it if someone could tell me where I went wrong and how to approach it.

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  • $\begingroup$ strictly as worded it sounds like one box has all 3 objects? if it reads as '2 or more' then consider 1 - P(at most one ball in each box)... $\endgroup$ – user136920 Jun 20 '14 at 9:15
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    $\begingroup$ For the analysis of the probabilities, to get the right answer you need to imagine that the objects are distinct and the boxes are distinct. $\endgroup$ – André Nicolas Jun 20 '14 at 14:51
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if the question is meant to read that one box has at least two objects... we'll subtract from one the probability that no box has more than one ball.

it doesn't matter where the first object is placed. the probability that the second object is in a different box than the first is 4/5, and the probability that the third is placed in a different box than the first two is 3/5. multiplying gives 12/25, which gives a final probability of 13/25.

if the question is meant to read that one box has all three objects, it doesn't matter where the first object is placed, the probability that the second and third objects are put in the same box is 1/5 each, so multiplying gives 1/25.

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