Q. 225.0( 1 Vote )

# Mark the correct alternative in the following:

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

A. 12^{2} – 1

B. 2^{12}

C. 2^{12} – 1

D. none of these

Answer :

In the room there are 12 bulbs of same wattage, each having separate switch.

We have 2 options for each bulb i.e. either switching it ON or to switching it OFF.

The 1^{st} bulb can be switched ON or OFF i.e. 2 choices.

The 2^{nd} bulb can be switched ON or OFF i.e. 2 choices, and so on.

Now, for 12 bulbs we have total 2^{12} choices.

But, as we have to illuminate the room, so the single choice in which all the 12 bulbs are OFF should be omitted.

So, we have total __(2 ^{12} – 1)__ ways to light the room with different amounts of illumination.

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