1996 AHSME Problem 10

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

\text{(A)}\ 12\qquad\text{(B)}\ 15\qquad\text{(C)}\ 24\qquad\text{(D)}\ 28\qquad\text{(E)}\ 56

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.