How many different ways can the students at a school select the president, vice president and secretary from a group of 5?

60 ways.
Explanation: Suppose that we had 5 people, A, B, C, D, and E, and we had to select a P, VP, and S.

For the President, we have 5 different selections.
If we choose a president, then we can only pick 1 from 4 people for the VP.
Using the same logic, we'd have 3 different choices for the S.

Hence, we have 5 · 4 · 3 different ways.

Alternatively, this is:

different ways.