## Counting Paths

When there are multipl paths from one town to another, with intermediate towns each being connected to another town by a path, we can find the total number of possible paths by using the product principle along each path.

To find the number of routes from P to Q,

Apply the product principle along PADQ:1*2*1=2

Apply the product principle along PBEGQ:1*3*2*1=6

Apply the product principle along PCFQ:1*3*1=3

The total number of paths from P to Q is 2+6+3=11