Question

50 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

The number of possible ways three medals can be distributed among 50 athletes is determined by a permutation calculation: 50 × 49 × 48, resulting in 117,600 possible ways.

Step-by-step explanation:

In order to determine the number of ways the 3 medals can be distributed among 50 athletes, we can use the concept of permutations. Since there are no ties and the order in which the medals are awarded is important (gold, silver, and bronze are different), we have a permutation problem.

The first place can be taken by any of the 50 athletes. Once the gold medalist is decided, there are 49 athletes left who can win the silver medal. After the first two places are taken, there are 48 athletes left for the bronze medal. Therefore, the number of different ways to award the three medals is 50 × 49 × 48.

The calculation is simply a permutation of 50 items taken 3 at a time (50P3), which gives us:

• 50 × 49 × 48 = 117,600

So, there are 117,600 possible ways the medals can be distributed.