SOLUTION: There are 8 swimmers in a race. In how many ways can they finish if there are no dead heats and the swimmer in Lane 2 finished after the swimmer in Lane 5? I'm not quite sure ho

Question 1138418: There are 8 swimmers in a race. In how many ways can they finish if there are no dead heats and the swimmer in Lane 2 finished after the swimmer in Lane 5?
I'm not quite sure how to solve this. Any help would be appreciated
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

This problem has unexpected and beautiful solution.

The number of permutations where #2 goes before #5 is exactly equal to the number of permutations where #2 goes AFTER #5,


so each of these numbers is half of 8!, which is the total number of all permutations of 8 objects.


ANSWER.  3*4*5*6*7*8 =  = 20160 ways.

RELATED QUESTIONS
There are 8 swimmers competing in a race. Prizes are awarded for the swimmers who finish... (answered by ewatrrr)

There are 6 swimmers in the finals of the backstroke competition.How many different ways... (answered by ewatrrr)

There are 25 people in a race. In how many ways can they finish in first and second... (answered by Fombitz)

eight swimmers are competing in a race. how many ways can the swimmers fill the top three (answered by ewatrrr)

There are four times as many swimmers as non swimmers . If there are twenty people in the (answered by Cromlix)

In a race in which 9 automobiles are entered and there are no ties,in how many different... (answered by fractalier)

In a race in which twelve automobiles are entered and there are no ties, in how... (answered by josmiceli)

hidori, cherie, ellis and morgan are running a race in how many different ways might they (answered by josmiceli)

How many ways are there for four Cricketers, three Swimmers and two Athletes be stand in... (answered by ramkikk66)