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  • In how many ways can 7 people be divided into 3 teams of 2, 2, and 3 people?  Option: 1 210<stro

In how many ways can 7 people be divided into 3 teams of 2, 2, and 3 people?

 

Option: 1

210


Option: 2

420


Option: 3

630


Option: 4

840


Answers (1)

To find the number of ways to divide 7 people into 3 teams of 2, 2, and 3 people, we can use combinatorics.

First, let's select a team of 2 people. We can choose 2 people out of 7 in different ways.

Next, we have 5 people remaining. Let's select the second team of 2 people from these 5. We can choose 2 people out of 5 in C(5, 2) ways.

Finally, we are left with 3 people. These 3 people will form the third team.

Therefore, the total number of ways to divide 7 people into 3 teams of 2, 2, and 3 people is:

\begin{aligned} & C(7,2) \times C(5,2) \\ = & \frac{7 !}{2 ! \times(7-2) !} \times \frac{5 !}{2 ! \times(5-2) !} \\ = & 21 \times 10 \\ = & 210 \text { ways. } \end{aligned}
So, there are 210 ways to divide 7 people into 3 teams of 2, 2, and 3 people

Posted by

Sumit Saini

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