Question

In an upcoming race, the top 3 finishers will be recognized with the same award. There are 12 people entered in the race.

How many ways can the top 3 racers be grouped from the 12 people?


There are __[blank]__ ways the top 3 racers can be grouped from the 12 people.


Any help is super appreciated. Thank you in advance

Answer 1

220

Explanation:

Given,

The total number of people = 12,

Out of which, top 3 finishers will be recognized with the same award,

So, the total possible way = total combination of 3 people out of 12 people

`=^(12)C_3`

`=(12!)/(3!(12-3)!)`

`=(12* 11* 10* 9!)/(3* 2* 9!)`

`=(1320)/(6)`

`=220`

Hence, there are 220 ways the top 3 racers can be grouped from the 12 people.