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Probability Level 3

there are 10 bulbs in a room

10 switches (all bulbs are distinct) in how many ways can the room be illuminated??


The answer is 1023.

Abhay Kanwar by Abhay Kanwar , 34, India

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2 solutions

Drop TheProblem
Sep 2, 2014

We have to find all the possible subsets (with 1,2,3,4.....10 elements) of the set of 10 elements. So we have 2^10 possibilities. We have to remove the case where all the switches are off. so the solution is 2^10-1=1023.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

It should say in the problem that all the lights being off does not count as a subset. While this could be claimed to be intuitive as it says "illuminated" it is still good to be clear.

Nicolas Bryenton - 6 years, 8 months ago
Noel Lo
Apr 16, 2015

Any positive whole number (1 to 10) of bulbs can be on LOL. Simply take 2 10 − 1 2^{10}-1 as the only case you need to discount is zero bulbs on.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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