Three distinct segments are chosen at random among the segments whose endpoints are the vertices of a regular 12-gon. What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area?
Answer Choices
A. \dfrac{553}{715}
B. \dfrac{443}{572}
C. \dfrac{111}{143}
D. \dfrac{81}{104}
E. \dfrac{223}{286}