Counting - Permutations

SOURCE:COMPETITION
Number of Problems: 2. : (Book)

 

 

1.
2.
 '

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)} 240qquadmathrm{(B)} 360qquadmathrm{(C)} 480qquadmathrm{(D)} 540qquadmathrm{(E)} 720

'