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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.

$\begin{array}{1 1}(A)\;10^2\\(B)\;1023\\(C)\;26{10}\\(D)\;10!\end{array}$

Given :
Total number of lamps =10
Since at least one lamp is to be kept switched on
The total number of ways are
$10C_1+10C_2+....10C_{10}$
$\Rightarrow 2^{10}-1$
$\Rightarrow 1024-1$
$\Rightarrow 1023$
Hence (B) is the correct answer.