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Permutations and Combinations
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} $
cbse
math
class11
ch7
permutations-and-combinations
exercise7-3
exemplar
q13
sec-b
medium
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asked
May 15, 2014
by
sreemathi.v
edited
May 9, 2016
by
meena.p
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1 Answer
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.
answered
May 15, 2014
by
sreemathi.v
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