Okay, I'll try again. There are some glaring faults with my previous answer... I guess it's a good thing I scheduled an afternoon test instead of a morning one!
combinations of one or both couples together:
multiply by 2 because of symmetry(e.g. 11322 flipped around is 22311): 7x2= 14.
multiply by two because couple one is nondistinct.
multiply by two because couple two is nondistinct.
Total ways to arrange couples = 5!=120
Probability of neither couple sitting together= 1-(7/15) = 8/15
I feel like I'm still missing something though...
Is it 1/10?
This is not very elegant, but here goes:
Ways to seat one or both couples together
Multiply by 2 because you can have the same combinations backward (due to symmetry). 6x2=12 ways to seat one or both couples together.
Total number of ways = 5!
12/5! = 1/10