In essence, how many unique ways can I choose a subset of N people such that there exist 3 people in the subset who are adjacent in the original set.
e.g. N = 4 Lets label the people {1,2,3,4} I can choose {1,2,3} , {2,3,4} , { 1,2,3,4} making a total of 3 ways.
Here I assume that {1,2,3} = {3,2,1} etc. are the same
Is there any general formula I can derive for calculating this?