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Answer the following: A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall. - Mathematics and Statistics

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प्रश्न

Answer the following:

A hall has 12 lamps and every lamp can be switched on independently. Find the number of ways of illuminating the hall.

बेरीज
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उत्तर

There are 12 lamps, i.e., n = 12.

Now, if at least one of the switches is 'on' the hall can be illuminated.

∴ the number of ways in which the hall can be illuminated = 2n – 1

= 212 – 1

= 4096 – 1

= 4095

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पाठ 3: Permutations and Combination - Miscellaneous Exercise 3.2 [पृष्ठ ६८]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 3 Permutations and Combination
Miscellaneous Exercise 3.2 | Q II. (11) | पृष्ठ ६८

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