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

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.

Solution:

Total number of lamps = 10

A lamp can be either switched on or switched off.

Since, at least one lamp is to be kept switched on,

$\therefore$ The total number of ways are $2^{10}-1=1023$.

Thus, the number of ways in which the hall can be illuminated are 1023.