Question 657302: There are 17 street lamps along a straight street. In order to save electricity and not affect the regular use at the same time, we can shut down 5 of these lamps, but we cannot turn off a lamp at either end of the street, and we cannot turn off a lamp adjacent to a lamp that is already off. Under such conditions, in how many ways can we turn off 5 lamps?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are 17 street lamps along a straight street. In order to save electricity and not affect the regular use at the same time, we can shut down 5 of these lamps, but we cannot turn off a lamp at either end of the street, and we cannot turn off a lamp adjacent to a lamp that is already off. Under such conditions, in how many ways can we turn off 5 lamps?
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List the digits 1,2,3,...16,17
1 and 17 cannot be shut off so the 5 OFF lights must be in 2,3,4...15,16
If 2 is OFF, turn off 4,6,8,10 or several other patterns
if 2 in on, turn off 3,5,7,9,11 or serveral other patterns
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I'll leave the counting to you.
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Cheers,
Stan H.
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