12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is

Step-by-step solution

Here, since each ball can be placed in any one of the 3 boxes, therefore there are 3 ways in which a ball can be placed in any one of three boxes. Thus, there are 3 12 ways in which 12 balls can be placed in 3 boxes. The number of ways in which 3 balls out of 12 can be put in the box is C 3 12 ​. The remaining 9 balls can be placed in 2 boxes in 2 9 ways. Hence, the required probability is C 3 × 2 9 12 3 12 .