Question

There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which hall can be illuminated is
1. 10²
2. 1023
3. 2¹⁰
4. 10!

Answer 1

Correct Answer - Option 2 : 1023

Given:

Total number of lamps = 10

Calculations:

There are two options for every light 

Hence, The number of combinations = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

⇒ 2¹⁰

At least one switch must be ON

Hence, The number of combinations = 2¹⁰ - 1

⇒ 1024 - 1 = 1023

∴ The required combinations are 1023