SOLUTION: a club has 10 light bulbs which can be switched on off separately. the number of ways in which the club can be lightened to different amount of illumination is - 2^10 or

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Question 756481: a club has 10 light bulbs which can be switched on off separately. the number of ways in which the club can be lightened to different amount of illumination is -
2^10 or 2^10 -1
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You have two possibilities for each lihght bulb: on or off.
The possible for the club are 2 X 2 X 2 X ... X 2 X 2 = 2%5E10, but that includes one case in which all light bulbs are off, and the club is in the dark.

The number of ways in which the club can be lighted to some amount and pattern of illumination is 2%5E10-1=1024-1=1023

That does not mean that there are 1023 different levels of energy consumption for the lighting. If all bulbs are of the same kind, you would have 10 different levels of energy consumption depending on how many light buls are on (1 through 10). If that is what you call "amount of illumination", then the answer is 10.

However, I think it would matter to people which bulbs are on, in addition to how many. For example, there are going to be 10 different situation where only one light bulb is on. If all bulbs are of the same kind, all 10 of those cases would mean about the same amount of energy consumption, but the areas with the most illumination would vary. Would you call those 10 cases different amounts of illumination?