Mark has to visit towns B and C in any order. The roads connecting these towns with his house are shown on the diagram. How many different routes can he take starting from A and returning to A, going through both B and C and not traveling any road twice on the same trip?
Options.
A) 5 B) 8 C) 9 D) 10 E) 12
Mark can travel clockwise or anticlockwise on the diagram.   Clockwise, he has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.   Similarly, anticlockwise she has four different routes.   Total routes = 8   8
<result>B</result>
Mark has to visit towns B and C in any order. The roads connecting these towns with his house are shown on the diagram. How many different routes can he take starting from A and returning to A, going through both B and C and not traveling any road twice on the same trip?