AMC 10 2008b Problem 21

Ten chairs are evenly spaced around a round table and numbered clockwise from $1$ through $10$. Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How many seating arrangements are possible? $\mathrm{(A)}\ 240 \mathrm{(B)}\ 360 \mathrm{(C)}\ 480 \mathrm{(D)}\ 540 \mathrm{(E)}\ 720$