【Example 2】 6 athletes participate in the final, with no ties for any positions. Find the number of possible outcomes where Athlete No. 1 does not come in sixth place.
Solving: Since there are no parallel rankings, the number of ranking situations for 6 athletes is 6!. If athlete No.1 gets the last place, the number of situations for the remaining 5 athletes to get the top five places is 5!. Therefore, by the method of exclusion, the number of situations where athlete No.1 does not get the last place is $6!-5!=5 \cdot 5!=600$ kinds.