1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Discrete mathematics question

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations



    3. The attempt at a solution

    I've looked at this question a few times now and I still don't even know where to begin. Any help would be highly appreciated.
     
  2. jcsd
  3. Sep 28, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Hmm .. I would start as follows:

    First, forget about the two end-lights. They're always on. That leaves 15 lights to worry about.

    How many ways can you arrange 15 distinguishable things taken 5 at a time?

    Then, how many states are prohibited by the "no 2 adjacent lights off" rule?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook