Question

68 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 3 medals be distributed?

Answer 1

To find the number of possible ways the 3 medals can be distributed, we can use the concept of permutations.

First, let’s determine the number of options for the gold medal. Since there are 68 athletes competing, there 68 possible choices for the gold medal winner.

Next, after the gold medal winner is determined, there are 67 choices for the second-place finisher.

Finally, after the gold and silver medals are awarded, there are 66 remaining athletes who can potentially win the bronze medal. Thus, there are 66 choices for the third-place finisher.

To find the total number of possible ways to distribute the medals, we multiply the number of choices for each medal: 68* 67* 66* = 314,136.

Therefore, there are 314,136 possible ways to distribute the gold, silver, and bronze medals among the 68 athletes in the race.