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  • 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. [Hint: Required number = 210 – 1].

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. [Hint: Required number = 210 – 1].

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The hall can be illuminated if atleast one lamp is switched out of 10 lamps  Total number of ways

=^{10}C_{1}+^{10}C_{2}+\cdots \cdot \ldots \ldots+^{10}C_{10}=2^{10}-1=1024-1=1023

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