Five students are running for Junior class president. They draw straws to see who will go first, second, etc. In how many different orders could they give their speeches?

Explanation:

There are 5 choices for the first selection, 4 choices for the second, etc etc until we reach 1 for the last selection. We have the countdown {5,4,3,2,1}. We'll multiply those values together to get our answer.

5*4*3*2*1 = 120

This operation of starting with some integer, counting down and multiplying along the way, is done so very often that it's given a name which is "factorial". The shorthand notation is to use an exclamation mark. So we'd say 5! = 120

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step-by-step explanation: