There are 10 lamps in a hall. Each one of the | vedclass

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(B) Each of the $10$ lamps has $2$ possibilities: it can either be switched 'on' or 'off'.Since there are $10$ lamps, the total number of combinations

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$1023$

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(B) Each of the $10$ lamps has $2$ possibilities: it can either be switched 'on' or 'off'.Since there are $10$ lamps, the total number of combinations for the state of the lamps is $2 	imes 2 	imes \dots 	imes 2$ ($10$ times), which equals $2^{10} = 1024$.However, the hall is illuminated only if at least one lamp is switched on.The only case where the hall is not illuminated is when all $10$ lamps are switched 'off'.Therefore, we subtract this $1$ case from the total number of combinations.Total ways to illuminate the hall = $2^{10} - 1 = 1024 - 1 = 1023$.

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

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