We want to count the number of distinct paths from node s to node t in the following directed graph. O O O O O O O O O 10 O O O O O 0 O O O 0 O O CO O The following figure shows three distinct paths from s to t. A path from s to t consists of exactly 12 edges. Both the blue path and the red path shown in the figure go through the vertex g. The green path does not go through the vertex g. Two paths are equal if and only if they both use the exact same 12 edges, and they are distinct otherwise. The three paths shown are thus distinct. O O O O a O O O 6 O O to O O O O CO 1. How many distinct paths are there from s to ? Show your calculations and justify your answer Simplify your answer as much as possible. 2. How many distinct paths are there from a to f that goes through the vertex labeled g? Show your calculations and justify your answer.