The Path Problem
Bob is on his way to the city. However, he lives in the rural country and he has no map. To get to the city there are 5 different intersections, and each have 5 different paths to take. only 1 specific choice of paths can take you to the city. What is the probability that out of chance, Bob will guess the correct combination of paths? (Assume Bob has no knowledge of the paths)
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1 solution
Let's start at the 5th intersection. Since there are 5 different paths to go from here, the possibilities are 5. Then go back to intersection 4, there are 5 different paths, each with 5 more paths to go, so 25 paths in total. Back in the third intersection, there are 5 different paths, each with 25 paths of their own, so 125 paths in total. In the second intersection, there are 5 different paths each with 125 paths of their own, so a total of 625 paths. Finally, at the first intersection, there are 5 paths each with 625 paths of their own, so 3125 paths total. This problem can be solved by doing the following calculation 5 to the fifth power. These sorts of problems can be solved by: # of intersections to the power of # of paths per intersection.