Question

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.

[Hint: Required number = 210 – 1].

Answer 1

We know that,

We also know that,

According to the question,

Number of lamps in a hall =10

Given that,

One of the lamps can be switched on independently

Hence, the number of ways in which the hall can be illuminated is given by,

C₁¹⁰ + C₂¹⁰ + C₃¹⁰ + C₄¹⁰ + C₅¹⁰ + C₆¹⁰ + C₇¹⁰ + C₈¹⁰ + C₉¹⁰ + C₁₀¹⁰

=2¹⁰-1

=1024-1

=1023