There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.

Explanation

To solve the problem of finding the number of ways to illuminate a hall with 10 lamps that can be switched on or off independently, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the States of Each Lamp**:
Each lamp can be in one of two states: either it is switched on (1) or switched off (0).

2. **Calculating Total Combinations**:
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