1. **Stating the problem:** Calculate the permutation $18P17$, which represents the number of ways to arrange 17 objects out of 18 distinct objects. 2. **Formula used:** The permutation formula is $$nP r = \frac{n!}{(n-r)!}$$ where $n$ is the total number of objects and $r$ is the number of objects to arrange. 3. **Apply the formula:** Here, $n=18$ and $r=17$, so $$18P17 = \frac{18!}{(18-17)!} = \frac{18!}{1!} = 18!$$ 4. **Simplify:** Since $1! = 1$, the value is simply $18!$. 5. **Interpretation:** This means the number of ways to arrange 17 objects out of 18 is equal to the total number of ways to arrange all 18 objects. 6. **Final answer:** $$18P17 = 18! = 6402373705728000$$