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?

A) 10
B) 8
C) 6
D) 4
E) 2

Here we can assume few possibilities

1st : - let us go to B first, then C and back to A, then we have the following possibilities-
From A to B we have 1 way
From B to C we have 2 ways
From C to A we have 2 ways

Total number of ways = 1*2*2 = 4

2nd - let us go to C first then B and then back to A, we have the following possibilities-
From A to C we have 2 way
From C to B we have 2 ways
From B to A we have 1 way

Total number of ways = 2*2*1 = 4

Total number of ways = 4+4 = 8
_________________

If you found this post useful, please let me know by pressing the Kudos Button