A permutation is an arrangement is which order is important. You can use the counting principle to count permutations.
This is a permutation problem since the order is important. The result can be represented as 12P3 which means the number of ways to choose and arrange three different (not repeated) places from a set of twelve horse.
There are 12 different horses that can come in first. Then, there are 11 different horses that can come in second. After that, there are 10 horses left that can come in third. Therefore, 12 times 11times 10 = 1320 different numbers. We can write this as 12P3.
There are 1,320 different ways to award the three places.
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