Agold, a silver, and a bronze medal are awarded in an olympic event. in how many possible ways can the medals be awarded for a 200-meter sprint in which there are 10 runner?

We can choose one of the 10 runners for the gold medal.

Then, we choose one of the remaining 9 runners for the silver medal.

Finally, we choose one of the remaining 8 runners for the bronze medal.

So, in total, we have

possible choices.