In a horse race, how many different finishes among the first 33 places are possible if 20 horses20 horses are running? (exclude ties)

To solve this problem, let us break this down one by one.

There are 20 possible horses that could win in first place. Therefore this means that for each of these possibilities, there are now 19 horses that could come in second. So meaning there are 20 x 19 possible combinations for the first 2 places.

20 x 19 = 380. And for each of those combinations, there are also 18 possible horses that could come in the third place. So

20 x 19 x 18 = 6,840

There are 6,840 possible horse combinations for the first 3 places in the race.