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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

Respuesta :

Answer:

220

Step-by-step 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

[tex]=^{12}C_3[/tex]

[tex]=\frac{12!}{3!(12-3)!}[/tex]

[tex]=\frac{12\times 11\times 10\times 9!}{3\times 2\times 9!}[/tex]

[tex]=\frac{1320}{6}[/tex]

[tex]=220[/tex]

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

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