Forty students are in the running for the science prize. In how many ways can a winner, a runner-up, and an alternate be chosen?

Answer 1

If you think about lining 40 students up in a line, and choosing one, the winner, you would have 40 students to choose from. But after you have chosen the winner, he/she cannot also be the runner-up nor the alternate. So now you only have 39 students from which to choose a runner up. And after choosing the runner up, then you only have 38 students left from which to choose an alternate.

So they can be chosen 40 * 39 * 38 = 59280

Or you can use the fact that this is a permutaion and use P(40,3) = 59280