How many ways can we turn off 5 lamps along a street?

[kts1230]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

I've looked at this question a few times and I still don't even know where to begin. Any help would be highly appreciated.

 

[SammyS]

Get out 17 toothpicks and a hotdog bun.

 

[zgozvrm]

Start with turning off #2, 4, 6, 8, & 10, then 2, 4, 6, 8, 11, then 2, 4, 6, 8, 12, etc. until you get to 2, 4, 6, 8, 16.
Then try 2, 4, 6, 9, 11, then 2, 4, 6, 9, 12, etc. to 2, 4, 6, 8, 16

Look for a pattern.