Twelve balls are distributed among three boxes, find the probability that the first box will contains three balls.

Explanation

Because each ball can be placed in any of the three boxes, there are two ways to place a ball in each of the three boxes.

As a result, there are three dozen different methods to arrange 12 balls in three boxes.

The number of ways in which 3 balls out of 12 can be put in the box is `text{}^{12} C_{3}`. The remaining 9 balls can be placed in 2 boxes in `2^{9}` ways.

So,required probability is

`frac{text{}^{12} C_{3}}{3^{12}} 2^{9}=frac{110}{9}(frac{2}{3})^{10}`