Question

66 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

274560

Explanation:

We can "choose" one of the 66 athletes for the gold medal. That athlete can't win any other medals, so there are 65 athletes left.

We can then "choose" one of the 65 athletes left for the silver medal. That athlete can't win any other medals, so there are 64 athletes left.

We can then "choose" one of the 64 athletes left for the bronze medal.

That leaves us with 66 possible choices * 65 possible choices * 64 possible choices=274560 possible choices