## Thinking Mathematically (6th Edition)

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. ----------- 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: $8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=8!=40,320$