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Sum of Coefficients of All Terms

In the hall t...

Question

In the hall there are ten bulbs and there ten buttons in how many ways this halls can be enlightened.

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Solution

Total no. of lamps $= 10$
Since at least one lamp is to be kept switched on,
The total number of ways are, $10 c_{1} + 10 c_{2} \dots \dots 10 c_{10}$
$2^{10} - 1 ⟹ 1024 - 1 ⟹ 1023$

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