In a particular 100 meter race, 9 athletes are participating that are numbered 1-9. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes? Choose one:
A) 102,330
B) 115,990
C) 132,220
D) 152,770
E) 181,440
The total number of ways for the athletes to finish is 9! = 362,880.   #4 will be ahead of #2 in exactly half of these possibilities.   362,880/2 = 181,440   The answer is 181,440.
<result>E</result>
In a particular 100 meter race, 9 athletes are participating that are numbered 1-9. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?