A race including 12 finalists is conducted at Courtyard Community College. Prizes for the first 3 places are awarded. How many different outcomes are there?

Question

directrix · Answer

Given that this is a race, then I assume order matters. So, if persons A, B, and C win in that order, then that is a different outcome from B, A, C.

There are 12 choices for the lst place. Once somebody is first, that leaves 11 choices for 2nd place, and likewise, 10 choices for third place.

According to the Fundamental Principle of Counting, there are 12*11*10 possible outcomes for the event. Multiply those three numbers to get the answer to your question.