SOLUTION: 3 ladies and 3 gents can be seated at a round table sothat any two and only two of ladies sit together number of ways is?

Algebra ->  Permutations -> SOLUTION: 3 ladies and 3 gents can be seated at a round table sothat any two and only two of ladies sit together number of ways is?       Log On


   

Question 895160: 3 ladies and 3 gents can be seated at a round table sothat any two and only two of ladies sit together number of ways is?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
When the problem says "round table", that means it's as if the table
and people were on a turntable floor.  So there are only these two
seating schemes where exactly 2 women sit together.


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

For each of these two arrangments there are 3! ways to place the women
and 3! ways to place the men.  Thats 3!*3! = 6*6 = 36 ways for each.
Since there are 2 seating schemes above, we double that number.  

Answer = 2*36 = 72

Edwin