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

As 1 lamp is also enough for the hall to be illuminated.

Total number of ways = ${}^{10}{C}_1{+}^{10}{C}_2+....{+}^{10}{C}_{10}$

$⟹2^{10}-1$

$⟹1024-1$

$⟹1023$