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.