# Probability with identical boxes and identical objects

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.

• 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)... – user136920 Jun 20 '14 at 9:15
• 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. – André Nicolas Jun 20 '14 at 14:51