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There are 10 lamps in a hall.Each one of...

There are 10 lamps in a hall.Each one of them can be switched on independently.Find the number of ways in which the hall can be illuminated.

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Total number of ways `= ""^(10)C_(1) + ""^(10)C_(2) + ""^(10)C_(3) + ""^(10)C_(4) + ""^(10)C_(5) + ""^(10)C_(6) + ... + ""^(10)C_(10)`
`= 2^(10) - 1" "` `[because ""^(n)C_(0) + ""^(n)C_(1) + ""^(n)C_(2) + ... = 2^(n)]`
`= 1024 - 1 = 1023`
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