Set Theoryhard
0:00.0
A school offers three extracurricular clubs: Robotics (), Drama (), and Athletics (). Each club has exactly 30 members. The school administration notices that:
- Any two of these clubs share at least 10 members.
- No student is a member of all three clubs.
Let be the maximum possible number of unique students who are members of at least one club, and let be the minimum possible number of such students. Determine the value of .
A school offers three extracurricular clubs: Robotics (), Drama (), and Athletics (). Each club has exactly 30 members. The school administration notices that:
- Any two of these clubs share at least 10 members.
- No student is a member of all three clubs.
Let be the maximum possible number of unique students who are members of at least one club, and let be the minimum possible number of such students. Determine the value of .