Question

In a room there are $12$ bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is equal to?

• A. ${12}^2-1$
• B. $2^{12}$
• C. $2^{12}-1$
• D. None of these

Answer 1

The correct option is C

$2^{12}-1$

Explanation for the correct option.

Find the required number of ways.

Each switch has two cases either it is ON or it is OFF.

To there be light in the room, atleast one bulb should be ON.

The number of ways of selecting ON or OFF are $2$ for each bulb.

So for $12$ bulbs the number of ways is $2^{12}$.

But in $2^{12}$ ways there will be one case in which all the $12$ bulbs are OFF and so there will be no light in the room.

So, the total number of ways to light the room such that the room has different amounts of illumination is $2^{12}-1$.

Hence, the correct option is C.