Question

In a track event with eight top-ranked runners, how many different ways can the runners finish the race?

A) 8
B) 16
C) 64
D) 128

Answer 1

There are 40,320 different ways the runners can finish the race.

Step-by-step explanation:

The number of different ways the runners can finish the race can be determined by using the concept of permutations. In this case, since there are eight runners and each runner can finish in a different position, we can calculate the number of permutations.

The formula for permutations is P(n,r) = n! / (n-r)! where n is the total number of objects and r is the number of objects selected. Here, n = 8 and r = 8, so the calculation becomes P (8,8) = 8! / (8-8)! = 8! / 0! = 8! / 1 = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320.

Therefore, there are 40,320 different ways the runners can finish the race.