In how many different way can 8 riders be matched up with 8 horses

The first rider could be with any of 8 horses.

the second rider could be with any of the remaining 7 horses

etc

so    8*7*6*5*4*3*2*1 = 8!  =

 $${\mathtt{8}}{!} = {\mathtt{40\,320}}$$

my goodness, that is a lot of ways :/

64 combinations