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  • A group of 16 people needs to be divided into 4 teams of 4 . In how many different ways can the teams be formed?Option: 1 <p style="list-style-type:lowe

A group of 16 people needs to be divided into 4 teams of 4 . In how many different ways can the teams be formed?

Option: 1

25,690,800

 


Option: 2

89,589,685

 


Option: 3

10,450,200

 


Option: 4

28,256,256


Answers (1)

best_answer

To calculate the number of different ways the 16 people can be divided into 4 teams of 4 , we can use combinations.

The number of ways to select 4 people from a group of 16 can be calculated as \mathrm{C(16,4)}, which represents " 16 choose 4 . " It can be calculated as:

\mathrm{ C(16,4)=16 ! /(4 ! \times(16-4) !)=16 ! /(4 ! \times 12 !)=(16 \times 15 \times 14 \times 13) /(4 \times 3 \times 2 \times 1)=1820 . }

Therefore, there are 1820 ways to form the first team.

After forming the first team, we are left with 12 people. Similarly, the number of ways to form the second team from these remaining 12 people can be calculated as \mathrm{C(12,4)=495.}

Next, after forming the first two teams, we are left with 8 people. The number of ways to form the third team from these remaining 8 people is \mathrm{C(8,4)=70.}

Finally, after forming the first three teams, we are left with 4 people. The number of ways to form the fourth 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:

\mathrm{ 1820 \times 495 \times 70 \times 1=25,690,800 }

Therefore, there are 25,690,800 different ways the 16 people can be divided into 4 teams of 4 .

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