A committee of students and teachers is being formed to study the issue of student parking privileges. Fifteen staff members and 18 students have expressed an interest in serving on the committee. In how many different ways could a five-person committee be formed if it must include at least one student and one teacher?

Question

A committee of students and teachers is being formed to study the issue of student parking privileges.  Fifteen staff members and 18 students have expressed an interest in serving on the committee.  In how many different ways could a five-person committee be formed if it must include at least one student and one teacher?

Reiny · Answer

can't have all staff or all sudents.
number of ways for all staff = C(15,5) = 3003
number of ways with all students = C(18,5) = 8568

With no restrictions = C(33,5) = 237336
So as stated above :
237336 - 3003 - 8568 = 225765

kitkat · Answer

Thanks:) I got the same answer