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  • A group of 10 people, including 3 managers and 7 employees, is going to sit at a round table for a meeting. If the managers must sit together, in how many different ways

A group of 10 people, including 3 managers and 7 employees, is going to sit at a round table for a meeting. If the managers must sit together, in how many different ways can they be arranged?

 

Option: 1

12,440

 


Option: 2

15,340

 


Option: 3

30,240

 


Option: 4

20,500


Answers (1)

To calculate the number of different ways the group of 10 people can be arranged at a round table, with the 3 managers sitting together, we can treat the group of managers as a single entity.

Now, we have 8 entities to arrange: the group of managers and the 7 employees.

The number of ways to arrange these 8 entities around a circular table is (8-1) !=7 !, since the circular arrangement is considered up to rotation.

However, within the group of managers, the managers themselves can be arranged among themselves. Since there are 3 managers, the number of ways to arrange them is 3 !.

Therefore, the total number of different ways to arrange the group of 10 people at the round table, with the managers sitting together, is:

7 ! \times 3 !=5,040 \times 6=30,240 .
Therefore, there are 30,240 different ways the group of 10 people can be arranged at the round table, with the managers sitting together.

Posted by

Sumit Saini

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