8. (10 points) 12 Smurfs are sitting around a round table, each Smurf hates the 2 Smurfs sitting next to him, but does not hate the other 9 Smurfs. Papa Smurf needs to send out a team of 5 Smurfs to rescue Smurfette, who was captured by Gargamel, and the team cannot include Smurfs who hate each other. There are $\qquad$ ways to form the team.
【Solution】Solution: According to the requirements, divide into three major categories:
One category is to select all odd-numbered ones, the number of groups is $C_{6}^{5}=6$,
The second category is to select all even-numbered ones, the number of groups is $C_{6}^{5}=6$,
The third category is a mix of odd and even numbers, which is more complex and further divided into 4 subcategories:
1st category: 1 even and 4 odd (or 4 odd and 1 even), the groups formed are: 2-5-7-9-11, 4-7-9-11-
2nd category: 2 even and 3 odd (or 3 odd and 2 even), the groups formed are: 2-4-7-9-11, 4-6-9-11-1, 6-8-11-1-3, 8-10-1-3-5, 10-12-3-5-7, 12-2-5-7-9, totaling 6 types.
3rd category: 3 even and 2 odd (or 2 odd and 3 even), the groups formed are: 2-4-6-9-11, 4-6-8-11-1, 6-8-10-1-3, 8-10-12-3-5, 10-12-2-5-7, 12-2-4-7-9, totaling 6 types.
4th category: 4 even and 1 odd (or 1 odd and 4 even), the groups formed are: 2-4-6-8-11, 4-6-8-10-1, 6-8-10-12-3, 8-10-12-2-5, 10-12-2-4-7, 12-2-4-6-9, totaling 6 types. According to the calculation method: $6+6+(6+6+6+6)=6+6+24=36$ (types). Therefore: There are a total of 36 methods to form teams.