Answer
See the explanation
Work Step by Step
To calculate the number of different paths through the 15 cities in the traveling salesperson problem, we need to compute the number of permutations. Since the salesperson must visit each city exactly once and return to the starting city, the number of paths can be calculated as (15-1)! = 14!, which equals 87,178,291,200 different paths.
To compute the length of all these paths assuming one microsecond per path, we need to multiply the number of paths by the time taken to compute the length of one path:
87,178,291,200 paths * 1 microsecond/path = 87,178,291,200 microseconds.
Therefore, it would take approximately 87,178.3 seconds or about 24.2 hours to compute the length of all paths.
