Question

A local college is forming a six-member research committee with one administrator, three faculty members, and two students. There are seven administrators, faculty members, and students in contention for the committee. How many six-member committees are possible

Answer 1

292600

Explanation:

A local college is forming a six-member research committee having one administrator, three faculty members, and two students. There are seven administrators, 12 faculty members, and 20 students in contention for the committee. How many six-member committees are possible?

`(7!)/((7 - 1)! 1!) * (12!)/((12 - 3)! 3!) *(20!)/((20 - 2)!2!)` = 292600

there are seven administrators, and only one is needed. thus there are 7 ways to choose 1 administrator.

there are 12 faculty members, and only 3 are needed. thus there are 12 ways to choose 3 members

there are 20 students and only 2 are needed. thus there are 20 ways to choose 2 students