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counting and probability intermediate

Problem

Ten chairs are evenly spaced around a round table and numbered clockwise from through . 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?
(A)
(B)
(C)
(D)
Solution
For the first man, there are possible seats. For each subsequent man, there are , , , or possible seats. After the men are seated, there are only two possible arrangements for the five women. The answer is .
Final answer
C