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].

Solution:

It is known that,

It is also known that,

As per the question,

10 = Number of lamps in a hall

Given,

Of the given lamps one lamp can be switched on independently

As a result, the no. of ways in which the hall can be illuminated is given by,