math300 statistics

Question

Fourteen athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the medals be distributed?

Answer 1

This is a permutations problem. Since order matters, and there are no repeats, we will have 3 slots (for the 3 possible placements). In 1st place, there could be 14 possible choices. In 2nd place, we would then have 13 possible choices left (no repeats/replacement). In 3rd place, we would then have 12 possible choices left. Therefore, there are 14 x 13 x 12 = 2184 possible ways the medals can be distributed.