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

Explanation

To solve the problem of finding the probability that the first box will contain exactly three balls when distributing twelve balls among three boxes, we can follow these steps:

### Step 1: Calculate the Total Number of Ways to Distribute the Balls
Each of the 12 balls can go into any of the 3 boxes. Therefore, for each ball, there are 3 choices. The total number of ways to distribute the 12 balls is given by:
\[ \text{Total ways} = 3^{12} \]

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