Q&A: Understanding Part C of a Round Trip Problem

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The discussion centers on the calculation of routes in a round trip problem, specifically part c, where the answer key indicates 14x13 as the solution. The user correctly identifies that there are 14 ways to reach point C but questions the return routes based on the roads taken. The confusion arises from the interpretation of restricted routes when certain roads are used in the outbound trip. The key takeaway is that the answer considers all possible combinations of outbound and return routes while adhering to the restrictions imposed by the roads used.

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I don't understand the answer for part c of the following question

View attachment 1615

The answer key gives 14x13 as the solution to part c. I understand there are 14 ways to get to point C but depending on which road can no longer be used, there is anywhere between 10 and 13 ways to return home. For example, say R8 was taken to get to C. Then there are 14-1 ways to make the return trip (just don't use R8). However, if R1R5 is used then we can't use either R1 (so now there are 3x3+2=11 ways to make the trip) or R5 (so now there are 2x4+2=10 ways to make the trip). What is wrong with my reasoning?
 

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As I understand the problem statement in c), if Linda takes R1R5 to get from A to C, there is a single trip she is not allowed to take back: R5R1. All other trips are allowed.
 

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