Question

How many line segments have both their endpoints located at the vertices of a given cube?

Answer 1

A cube has 8 vertices. Number of line portions = 8C2=28. (As a line portion has 2 end points)

(1) Each line fragment extraordinarily decides a couple of endpoints. (2) Each pair of endpoints interestingly decides a line section. The main perception ensures that you haven't "overlooked" any sections in your tallying. The second ensures that you haven't numbered any of the sections more than once.