Horse Race Permutations

At the start of a horse race, there are 12 distinct horses in the field. 3 horses can place at the end of the race, and it matters what order the horses placed in. For example, if horses \(\text{A},\) \(\text{B},\) and \(\text{C}\) placed, then it would matter which horse came in \(1^\text{st}, 2^\text{nd},\) and \(3^\text{rd}.\) The order \(\text{ABC}\) would be different than \(\text{ACB}.\)

How many possible fields of placed horses are there?

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