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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Sum

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

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Solution

Every lamp is either ON or OFF.
There are 12 lamps
Number of instances = 212
This number includes the case in which all 12
lamps are OFF.
∴  Required Number = 212 – 1 = 4095

Concept: Concept of Factorial Function
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Chapter 6: Permutations and Combinations - Miscellaneous Exercise 6 [Page 93]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Miscellaneous Exercise 6 | Q 14 | Page 93
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