SOLUTION: what is the soletion of in how many ways 7 man and 7 womenv can be seateted around table such that no two women can sit tgether

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Question 1073173: what is the soletion of in how many ways 7 man and 7 womenv can be seateted around table such that no two women can sit tgether
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
The only way is to seat them alternating men and women,
so no two men sit together either.  

Seat the 7 men first.

It would be 7! ways to seat the men, but we must divide
by 7 since the table and people are assumed to be sitting on 
a turntable that can be rotated 7 different ways. Therefore 
7! counts the number 7 times too many, so there are 7!/7 or 
6! ways to seat the men.
     


            M   
       M         M
                  
      M           M
                  
         M     M



Now for each of those 6! circular permutations, there
are 7 chairs in which to seat the 7 women. So they
can be seated any of 7! ways.

         W  M  W
       M         M
      W           W
      M           M
       W         W  
         M  W  M

So the answer is 6!7! = 3628800  ways.

Edwin
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