Permutations without Repetition

• 1st place - 3 possible choices
• 2nd place - 2 students remain who are eligible
• 3rd place - 1 remaining student will receive it.

To get the total number of possibilities, you again multiply by the number of available options each time, but since there's no repetition, the number goes down each time. In the above case, there are:
3 x 2 x 1 = 6 possible arrangements of the contestants.
This is also known as 3! or "3 factorial". Given a number N, N! means N factorial, the product of all the positive integers less than equal to N. So 5! = 5 x 4 x 3 x 2 x 1 = 120.

Whenever you need to arrange N items in order, there will be one less element available after each selection, so there there will be N! total ways to do arrange everything.