Question: In how many different ways can 4 married couples coming to a dinner be seated at a round table of eight seats (two seating arrangements

In how many different ways can 4 married couples coming to a dinner be seated at a round table of eight seats (two seating arrangements are equivalent if everyone has the same immediate left and right neighbors).

(1) if there are no restrictions?

(2) if each married couple is seated together?

(3) if the members of each sex are seated together?

(4) Assume the eight people are seated randomly. Compute the probability P("each married couple is seated together or the members of each sex are seated together").

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