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:

11322

11223

22113

11232

22131

12231

21132

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.

14x2x2=56

Total ways to arrange couples = 5!=120

56/120=7/15

Probability of neither couple sitting together= 1-(7/15) = 8/15

I feel like I'm still missing something though...

praetorian123 wrote:

jlyngal wrote:

Is it 1/10?

This is not very elegant, but here goes:

Ways to seat one or both couples together

11223

22113

11232

22131

11322

22311

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

nope...not correct.