Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?  Pick one.
A) 6!*7!
B) 136!*7!
C) 356!*7!
D) 366!*7!
E) 566!*7!
Yes, the solution given above is correct. Think of it this way:   There are 7 men: Mr. A, Mr. B .....   and 7 women: Ms. A, Ms. B ....   14 seats around a circular table.   You seat the 7 women such that no two of them are together so they occupy 7 non-adjacent places in 6! ways. For the first woman who sits, each seat is identical. Once she sits, each seat becomes unique and when the next woman sits, she sits in a position relative to the first woman (e.g. 1 seat away on left, 3 seats away on right etc)   The 7 men have 7 unique seats to occupy. Each of the 7 seats are unique because they have a fixed relative position (e.g. between Ms. A and Ms. B or between Ms. C and Ms. B etc...). So the men can sit in 7! ways.   Total 6!*7! ways.   6!*7!NS:6!*7!
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Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?