SOLUTION: There are four gentleman and three ladies who are to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?

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Question 887964: There are four gentleman and three ladies who are to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Since this is a round table, all 7 of these ways of placing
the men and the women below are considered the same.  

                  


[Don't ask me why, for they all seem different to me.  I 
wouldn't consider them the same myself, unless the chairs
and the table were all on top of a big turntable in the
floor. But I just happen to know that when a math problem 
talks about a round table, it means that the rotations 
are all considered to be the same seating arrangement. 
Hahahahaha!] 

We can arrange the 4 men 4! ways and the 3 women 3! ways.

Answer: 4!*3! = 24*6 = 144 ways.

Edwin