Question

if 3 identical trophies are awarded to the top 3 runners, how many possible winners are there in a race with 23 runners?

Answer 1

Solution:

Given:

Total runners = 23

3 identical trophies are awarded to the top 3 runners.

We have to find number of possible winners are there in a race with 23 runners.

First place can be achieved by any one of the 23 runners, so we have 23 ways for first place.

Second place can be achieved by any one of the remaining 22 runners, so we have 22 ways for second place

and third place can be achieved by any one of the remaining 21 runners, so we have 21 ways for third place.

Thus

Total number of possible winners = 23 X 22 X 21

Total number of possible winners = 10626

We can find same answer by using Permutation formula: