You can
put this solution on YOUR website! .
In how many different ways can 8 riders be matched up with 8 horses?
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For the 1st rider, there are 8 options.
For the 2nd rider, there are 7 options.
For the 3rd rider, there are 6 options.
. . . and so on . . .
In all, there are 8! = 8*7*6*5*4*3*2*1 different ways. ANSWER
Solved.
The answer in the post by @lynnlo is incorrect.
My post is written as opposition to that by @lynnlo.