3balls are placed in 3 boxes at random. what is the probability that exactly 2 boxes remain empty

If 2 boxes remain empty, it means that we put all three balls in one single box.

Suppose the full box is box number 1. For each ball, we have three choices - we may put it in box number 1, 2 or 3. This means that each box has a 1/3 chance of receiving each ball.

So:

So, the probability of putting all balls in box 1 is

But this is the probability of putting all ballx in box 1, and you can repeat this logic for box 2 and 3.

So, the probability of putting all balls in one single box is 1/27 for each box, for a total of

tangent

step-by-step explanation: