Answer:
40,320 orders.
Step-by-step explanation:
By using the multiplication rule of counting, the sales representative has 8 choices for the first city, 7 choices for the second, 6 choices for the third, 5 choices for the fourth, 4 choices for the fifth, 3 choices for the sixth, 2 choices for the seventh, leaving just one city left to visit as the eight. Therefore, the number of different orders that the visits can be arranged is:

There are 40,320 different possible orders.