1. **State the problem:** We want to find how many different possible finishes there are for the first 3 places in a horse race with 18 horses, excluding ties. 2. **Formula used:** This is a permutation problem because the order of the horses in the first 3 places matters. The number of permutations of $n$ items taken $r$ at a time is given by: $$P(n,r) = \frac{n!}{(n-r)!}$$ 3. **Apply the formula:** Here, $n=18$ (horses) and $r=3$ (places). $$P(18,3) = \frac{18!}{(18-3)!} = \frac{18!}{15!}$$ 4. **Simplify the factorial expression:** $$\frac{18!}{15!} = 18 \times 17 \times 16$$ 5. **Calculate the product:** $$18 \times 17 = 306$$ $$306 \times 16 = 4896$$ 6. **Final answer:** There are **4896** different possible finishes for the first 3 places among 18 horses, excluding ties.