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.

Answer 1

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,

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

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