Vishal Kumar wrote:

I thought it like this.

Suppose 1st if off then total no of ways to 2nd the room:

1*2*2. = 4.

Similarly if 2nd or 3rd is off.

So total no of ways : 4+4+4 = 12.

Although, this option is not there. Please correct me where did I go wrong .

Hi,

1*2*2...

The TWO in 1*2*2 includes when all three will be off and at that the room will not be lighted..

You are approaching the Q in a wrong way...

Room can be lighted in 3 ways..

1) all three on.. One way

2) two lights on.. choose two out of three 3C2...3 ways..

3) only one light on.. 3 ways

Total 1+3+3=7..

The way you are approaching, you could do it the following way..

The switch can be in two positions ON or OFF..

So total ways are 2*2*2=8, but these include the one instance when all three are OFF and at this time the room will not be lighted..

So 2*2*2-1=7

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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