Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip? Choose the correct choice from the following:
A) 7
B) 8
C) 6
D) 5
E) 4
Explanation:   Amy can travel clockwise or anticlockwise on the diagram.   Clockwise, she 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   Answer: 8
<result>B</result>
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?