Question

A college math department consisting of 9 faculty members must choose a department head, an assistant department head, and a faculty senate representative. in how many ways can this be done?

Answer 1

The department consists of 9 members but they must select a department head, an assistant department head, and a faculty senate representative. So they are 3 positions to be occupied by 9 people. It can be done in nPr = n! / (n - r)! ways.
So 9C3 ways. 9! / (9-3)! = 9! / 6! = 504 ways