Question

Eight 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

There are 336 possible ways to distribute the 3 medals among the 8 athletes.

Step-by-step explanation:

In this problem, we need to find the number of possible ways to distribute 3 medals (gold, silver, and bronze) among 8 athletes. Since the order of distribution matters (the gold medal winner is different from the silver medal winner), we can use the concept of permutations to solve this problem.

The number of permutations of r objects taken from a set of n objects can be calculated using the formula:

P(n, r) = n! / (n - r)!

In this case, we want to calculate P(8, 3) since we have 8 athletes and we are selecting 3 of them to receive medals. Plugging in the values into the formula:

P(8, 3) = 8! / (8 - 3)!

= 8! / 5!

= (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (5 × 4 × 3 × 2 × 1)

= 8 × 7 × 6 = 336