1. The problem statement, all variables and given/known data The question says that : Twelve distinct balls are distributes among three distinct boxes. Find the probability that the first box contains 3 balls. 2. Relevant equations None 3. The attempt at a solution It can be done through: No. Of choices for each ball=3 Total no. of choices=312 We have to select 3 out of twelve and arrange the remaining nine balls in 29 ways so that the answer would be : 110×210/312. But I was thinking that why a choice is given to the balls. Why not to boxes? Each box then will have 12 choices and total choices would be 123. Why this thinking is incorrect here?