Suppose that PQRSTUVW is a regular octagon. (A regular\:octagon is an octagon with eight equal side lengths and eight equal interior angles.) There are 70 ways in which four of its sides can be chosen at random. If four of its sides are chosen at random and each of these sides is extended in nitely in both directions, what is the probability that they will meet to form a quadrilateral that contains the octagon?
Answer Choices
A. \frac12
B. \frac{19}{35}
C. \frac{37}{70}
D. \frac{17}{35}
E. \frac{18}{35}