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  • A group of 8 friends, including 4 men and 4 women, is going to sit at a rectangular table. If the men and women must alternate seats, in how many different ways can they be seated?<div class='q

A group of 8 friends, including 4 men and 4 women, is going to sit at a rectangular table. If the men and women must alternate seats, in how many different ways can they be seated?

Option: 1

622


Option: 2

450


Option: 3

576


Option: 4

966


Answers (1)

best_answer

To calculate the number of different ways the group of 8 friends can be seated at a rectangular table, with the men and women alternating seats, we can treat the men and women as separate entities.

Since there are 4 men and 4 women, we can arrange them in the following pattern: MWMWMWMW.

Now, let's consider the number of ways to arrange the men among themselves and the women among themselves.

The number of ways to arrange the men among themselves is given by 4 !, and the number of ways to arrange the women among themselves is also given by 4 !.

Therefore, the total number of different ways to arrange the group of friends at the rectangular table, with the men and women alternating seats, is:

4 ! \times 4 !=24 \times 24=576 .

Therefore, there are 576 different ways the group of 8 friends can be seated at a rectangular table, with the men and women alternating seats.

Posted by

shivangi.bhatnagar

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