Question

There are twelve bulbs in a hall, each one of them can be switched independently. The number of ways in which the hall can be illuminated is

• A. ${12}^2$
• B. 4095
• C. $2^{12}$
• D. 12!

Answer 1

Answer: (B)

4095

The room can be illuminated even if one bulb is illuminated and for each bulb there are 2 choices of being ON or OFF and there are 12 bulbs.
So, number of ways in bulbs can be lighted $=2^{12}$
But, in the above cases, there is one single case in which all the bulbs are off and the room is not illuminated.
So, number of ways of illuminating the room $=2^{12}-1$