There are 15 runners in a race. Prizes are awarded to first, second, and third place. In how many different ways can the prizes be awarded?

Answer 1

Because the order of who gets which prize matters, we will use permutation. We are choosing 3 winners out of 15 runners, so: nPr = n! / (n-r)!

15 P 3 = 15! / 12! = 2730

If you have a TI 83/84 calculator, you can enter "15", hit "MATH", go to "PRB" tab by using the arrow keys, go to nPr, then enter "3".