How many ways can 12 horses in a race come in first second and third place?

A permutation is when order matters. In this case, you can't have any ties: you can only have one person for first place, one person for second place, and similarly one person for third place. Therefore, there are 12 horses competing for first place, 11 competing for second place (since one has already won first place), and 10 competing for third place (since two out of the 12 have won first and second places). Multiply the three to get the number of ways.