IKMC 2012 - Grades 9-10 - Self-study Question 30

Question 30

A, B, C, D, E, F, G, H are consecutive vertices of a convex octagon. Independently choose a vertex from C, D, E, F, G, H and join it to A; choose again from those six and join it to B. What is the probability these segments divide the octagon into exactly three regions?

$1/6$
$1/4$
$4/9$
$5/18$
$1/3$