In how many ways 5 different balls can be arranged into 3 different boxes so that no box remains empty?

Explanation

To solve the problem of arranging 5 different balls into 3 different boxes such that no box remains empty, we can break the solution down into systematic steps.

### Step-by-Step Solution:

1. **Identify the distributions**:
We need to find the possible distributions of the balls into the boxes such that no box is empty. The possible distributions are:
- 3 balls in one box, 1 ball in another box, and 1 ball in the third box (3, 1, 1).
- 2 balls in one box, 2 balls in another box, and 1 ball in the third box (2, 2, 1).
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