Answer
There are 40,320 different trips.
Work Step by Step
1st city: 8 choices.
2nd city: 7 choices.
3rd city: 6 choices.
4th city: 5 choices.
5th city: 4 choices.
6th city: 3 choices.
7th city: 2 choices.
8th city: 1 choice.
Using the Multiplication Rule of Counting (see page 298) with fatorial:
$8\times7\times6\times5\times4\times3\times2\times1=8!=40,320$
