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

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

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Cora 1 week 2021-09-15T19:48:44+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T19:49:53+00:00

    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

    =^{12}C_3

    =\frac{12!}{3!(12-3)!}

    =\frac{12\times 11\times 10\times 9!}{3\times 2\times 9!}

    =\frac{1320}{6}

    =220

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

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