Answer
40,320
Work Step by Step
The Fundamental Counting Principle$:$
The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur.
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Once a person for the lineup is chosen, there is one less left to choose from.
1. The 1st person in the lineup can be chosen in 8 ways.
2. The 2nd person in the lineup can be chosen in 7 ways.
3. The 3rd person in the lineup can be chosen in 6 ways.
4. The 4th person in the lineup can be chosen in 5 ways.
5. The 5th person in the lineup can be chosen in 4 ways.
6. The 6th person in the lineup can be chosen in 3 ways.
7. The 7th person in the lineup can be chosen in 2 ways.
8. The 8th person in the lineup can be chosen in 1 ways.
Total ways to arrange the lineup:
$8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=8!=40,320$
