Question

There are two job openings for similar staff positions at a certain college: one in the Registrar's Office, and one in the Office of Admissions. The Human Resources Department has identified five equally qualified candidates for the jobs (Jose, Tayo, Habib, Yu Yan, and Sara) and for fairness decides to choose two of the five candidates at random. The first chosen will fill the position in the Registrar's Office, and the second will fill the position in the Office of Admissions. How many ways can these two positions be filled?

Answer 1

For the position in the Registrar's Office, there are 5 options of candidates from which one will be chosen. So number of possible ways the position in the Registrar's Office can be filled = 5

For the position in the Office of Admissions, there are 4 remaining options from which one will be chosen. So number of possible ways the position in Office of Admissions can be filled = 4

So number of ways these two positions can be filled = 54 = 20