Question

Fifteen 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

Answer:

In 2730 ways medal can be distributed

Explanation:

We have given there are total 15 athletes are running in the race

So total number = 15

We have to choose 1 gold medal winner, 1 silver medal winner and 1 bronze medal winner

Means we have to select 3 athletes from 15 athletes

So number of way of selection will be $^{15}P_3$

$^{15}P_3=\frac{15!}{(15-3)!}=\frac{15!}{12!}=\frac{15\times 14\times 13\times 12!}{12!}=2730$

So in 2730 ways medal can be distributed