AMC 10B 2013 Problem 12

Let S be the set of sides and diagonals of a regular pentagon. A pair of elements of S are selected at random without replacement. What is the probability that the two chosen segments have the same length?

Answer Choices
A. \dfrac{2}{5}
B. \dfrac{4}{9}
C. \dfrac{1}{2}
D. \dfrac{5}{9}
E. \dfrac{4}{5}