The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrators, 8 faculty members, and 20 students are eligible to serve. How many different committees are possible?

Step-by-step explanation:

4 administrator are eligible and the student relations committee has only 2 administrator there are C (4,2) ways of choosing the administrators for the student relations committee

similarly for faculty members ways (8,3) and for students C (20,5)

the number of possible committee = 4!/2!2! * 8!/3!5! * 20!/5!15!

= 6 * 56 * 15504

= 5,209,344