In how many ways can you seat the 12 people at 3 round tables such that:
A) All couples are seated together. (the two members of each couple sit side-by-side)
B) No couples sit together.
I've tried this question several ways, but keep getting different answers.
Since it is a round table problem, I've set the first seat arbitrarily and proceeded from there. Any help would be greatly appreciated.
Edit: For (A), I found that any two couples can be seated side-by-side 2 ways, thus I got 4*(4 choose 2) = 24 ways to seat the couples at two tables. Moreover, I found 6 ways of seating the 4 single people at the third table (by placing one person arbitrarily in the first seat, leaving 3 options for the second seat, 2 for the third, and 1 for the last).