Combinations

Given conditions:

• cannot be in team X.
• cannot be in team Y.

Case 1:

The other member of team X is chosen from the remaining 7 students:

The remaining 7 students are divided into teams Y and Z:

The remaining 4 students are automatically in team Z (only 1 way to place them).

Total ways in this case:

Case 2:

The other 2 members of team X are chosen from the remaining 7 students (excluding ):

Now, is included in the remaining 7 students for teams Y and Z. Team Y (3 members) is chosen from the remaining 8 students, including :

The remaining 4 students are automatically in team Z (only 1 way to place them).

Total ways in this case:

Total Number of Ways

Final Answer: 665