There is a river with an island and five bridges. 
On one side of the river is a monastery, and on the other side is seen a monk in the foreground. 
The monk has decided that he will cross every bridge once, and only once, on his return to the monastery. 
This is, of course, quite easy to do, but on the way he thought to himself, "I wonder how many different routes there are from which I might have selected." 
Could you have told him? 
You will find that the difficulty is twofold: you have to avoid dropping routes on the one hand and counting the same routes more than once on the other.