There are 10 lamps in a hall. Each one of them can be switched on inde

1.	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.
Answer» There are 10 lamps in a hall. The hall can be illuminated if at least one lamp is switched. .'. Total number of ways = ¹⁰C₁ + ¹⁰C₂ + ¹⁰C₃ … + ¹⁰C₁₀ = 2¹⁰ – 1 = 1024 - 1 = 1023

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.

Answer»

There are 10 lamps in a hall.

The hall can be illuminated if at least one lamp is switched.

.'. Total number of ways = ¹⁰C₁ + ¹⁰C₂ + ¹⁰C₃ … + ¹⁰C₁₀

= 2¹⁰ – 1 = 1024 - 1 = 1023