Answer
1320
Work Step by Step
We have to pick first, second and third positions from among 12 horses. It is equivalent to finding the number of 3-permutations of a set with 12 elements. It is P(12, 3) by definition.
So, P(12, 3) = $\frac{12!}{(12-3)!}$ = $\frac{12\times11\times10\times9!}{9!}$
= $12\times11\times10$
=1320
[It can also be seen as this: We have 12 options to choose from for winner. For second, we have only 11 choices and for third, we have 10 choices left]
