The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.

The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!

Now, 7 men in a circle can be arranged in (7-1)! ways and if we place 7 women in empty slots between them then no two women will be together. The # of arrangement of these 7 women will be 7! and not 6! because if we shift them by one position we'll get different arrangement because of the neighboring men.

So the answer is indeed 6!*7!.

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Hope it helps.
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Just one question here.........since you will be seating the women also round the circular table, then why is that the logic of no. of asymmetric circular permutations of n objects does not apply here...?

Are you sure about that??

Why are women not considerad also circular???

FYI, the answer choices are missing from this question.

Thanks Bunuel !