Consider the network shown in the image. A double headed arrow i↔ j indicates that there is an edge i → j and an edge j →i. a) Compute the number of paths consisting of exactly 10 edges, which start at the vertex 1, end at the vertex 2, and do not pass through the vertex 3. b) Compute the number of paths consisting of exactly 10 edges, which start at the vertex 1, end at the vertex 2, and pass through the vertex 3 at least once. Enter your answer to part a): Enter your answer to part b): 5 4 3

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