Who is asking: Parent
Level: Secondary
Question:
If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Is there a formula for this?
Hi Kay,
We need more details to answer the question properly. Are they at a rectangular table with no one on the ends? Are the 'sides' different in any way? Or at a circular table with a head chair or with no 'head' chair?
These thing s make a difference.
Suppose it is just an rectangular table and people sit along the sides and there's a big picture on the wall along one side. There are 5! =120 ways to order the 'couples' along a side and this needs to be combined with 2 possibilities for each couple - which one of them is on which side (near the picture). In total 25 (5!) = 32 
120 = 3840 ways.
Penny