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A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.

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A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.

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Every lamp is either ON or OFF.

There are 12 lamps

Number of instances = 212

This number includes one case in when all 12 lamps are OFF.

∴ Required Number of ways = 212 – 1 = 4095

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