Question

There are 12 horses in a race. In how many ways can all the horses finish?

Answer 1

1st is 1 of 12.
Then 1 of 11, then 1 of 10
----
= 12*11*10 = 1320 ways

Answer 2

12 horses to fill 3 positions 

12 horses to fill 1st opening , when filled 

leaves 11 horses to fill 2nd opening , when filled 

leaves 10 horses to fill 3rd opening 

12 * 11 * 10 ways to fill the 3 spots