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  • A group of 12 people needs to be divided into 3 teams of 4. In how many different ways can the teams be formed?Option: 1 12,500  </di

A group of 12 people needs to be divided into 3 teams of 4. In how many different ways can the teams be formed?

Option: 1

12,500
 


Option: 2

15,200
 


Option: 3

10,475
 


Option: 4

34,650


Answers (1)

best_answer

To calculate the number of different ways the 12 people can be divided into 3 teams of 4 , we can use combinations.

The number of ways to select 4 people from a group of 12 can be calculated as\mathrm{C(12,4),} which represents \mathrm{" 12 \, \, choose \, \, 4 . "} It can be calculated as:

\mathrm{ C(12,4)=12 ! /(4 ! \times(12-4) !)=12 ! /(4 ! \times 8 !)=(12 \times 11 \times 10 \times 9) /(4 \times 3 \times 2 \times 1)=495 }

Therefore, there are 495 ways to form the first team.

After forming the first team, we are left with 8 people. Similarly, the number of ways to form the second team from these remaining 8 people can be calculated as \mathrm{C(8,4)=70}

Finally, after forming the first two teams, we are left with 4 people. The number of ways to form the third team from these remaining 4 people is \mathrm{C(4,4)=1.}

To find the total number of ways the teams can be formed, we multiply the number of ways for each team:

495 \times 70 \times 1=34,650 .

Therefore, there are 34,650 different ways the 12 people can be divided into 3 teams of 4 .

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Rishabh

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