In a particular 100 meter race, 8 athletes are participating that are numbered 1-8. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?  Choose the correct choice:
A) 14,540 B) 16,580 C) 18,920 D) 20,160 E) 24,320
The total number of ways for the athletes to finish is 8! = 40,320.   #4 will be ahead of #2 in exactly half of these possibilities.   40,320/2 = 20,160   The answer is 20,160.
<result>D</result>
In a particular 100 meter race, 8 athletes are participating that are numbered 1-8. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?