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  • A group of 9 friends, including 4 men and 5 women, is going to sit at a circular table. If the men and women must alternate seats, in how many different ways can they be

A group of 9 friends, including 4 men and 5 women, is going to sit at a circular table. If the men and women must alternate seats, in how many different ways can they be seated?

 

Option: 1

48


Option: 2

64


Option: 3

32


Option: 4

24


Answers (1)

best_answer

To calculate the number of different ways the group of 9 friends can be seated at a circular table, with the men and women alternating seats, we can fix the position of one person (let's say a man) and arrange the rest of the individuals relative to this fixed position.

Since there are 4 men and 5 women, we have the following pattern: MWMWMWMWM.

Now, let's consider the number of ways to arrange the remaining individuals (4 women) among themselves. The number of ways to arrange 4 women in a row is given by 4 !.

Therefore, the total number of different ways to seat the group of 9 friends at a circular table, with the men and women alternating seats, is:

4 !=24

Therefore, there are 24 different ways the group of 9 friends can be seated at a circular table, with the men and women alternating seats.

Posted by

Divya Prakash Singh

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