Question

In how many ways 6 men and 6 women sit at a round table so that no two men are
together?​

Answer 1

Answer:

Assuming a round table with 12 chairs, the 1st person, man or woman, has a choice of 12 chairs and picks 1. Because of the circular arrangement, this chair becomes an anchor and counts as just one choice because all possible permutations of seating relative to the chair selected are identical for any of the other 11 chairs as could have been selected, relative to those being seated. If this 1st person happens to be a man, Then the remaining men have 5! ways (permutations) of seating in order to be separated from one another. The 6 women are then left with 6! ways of being seated. Additionally, if the 1st person to choose a chair happens to be a woman, then women have 5! ways to be seated and men 6! ways. Therefore the total of ways to seat 6 men and 6 women such that no men sit together = 2*(6!)(5!) = 172,800.

If there were to be no constraints regarding the seating of 6 men and 6 women the permutations of occupying 12 chairs in a circular arrangement would be 11!=39,916,800

Step-by-step explanation:

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