Question

At a track meet, there are 8 runners competing in the 400-meter race. How many ways can the runners finish the race? (Assume all of the runners finish, and there are no ties.)

1) 3! = 336
2) 8! = 40,320
3) 3! = 6
4) 8! = 5,040

Answer 1

The number of ways the runners can finish the race is given by 8 factorial, which is equal to 40,320.

Step-by-step explanation:

The number of ways the runners can finish the race can be found by calculating the number of permutations of the 8 runners. Since all of the runners must finish and there are no ties, this is a permutation problem. The number of permutations of a set of objects can be calculated by finding the factorial of the number of objects. In this case, there are 8 runners, so the number of ways they can finish the race is given by 8! (8 factorial).

We can calculate 8! as 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320. Therefore, the correct answer is option 4) 8! = 40,320.