Problem

Sally lives in City A and works for the department of transportation. She needs to inspect the weigh stations in each of eight cities other than City A. In how many ways can she reach each of these cities and return to her home in City A? $\square$ (Simplify your answer.) Next

Solution

Step 1 :This problem is a classic example of a permutation problem in combinatorics. Sally has to visit each of the 8 cities once and only once, and then return to her home city. This is equivalent to finding the number of permutations of 8 distinct objects, which is given by 8!. However, since she can start her journey from any of the 8 cities, we need to multiply this by 8 to get the total number of ways she can inspect all cities and return home.

Step 2 :Calculate the total number of ways as \(8 \times 8!\)

Step 3 :The total number of ways is \(322560\)

Step 4 :Final Answer: \(\boxed{322560}\)

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Source: https://solvelyapp.com/problems/PME6otDQ7p/

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