In how many ways 10 different balls can be put in 2 difference boxes ?

Explanation

To solve the problem of how many ways 10 different balls can be put into 2 different boxes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Elements**: We have 10 different balls, which we can label as \( B_1, B_2, B_3, \ldots, B_{10} \). We also have 2 different boxes, which we can label as \( A_1 \) and \( A_2 \).

2. **Choices for Each Ball**: Each ball has 2 choices: it can either go into box \( A_1 \) or box \( A_2 \).

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