Data Management

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At a banquet, 4 coupes are sitting along one side of a table with men & women alternating.

a) how many seating arrangements are possible for these eight people?

b) how many arrangements are possible if each couple sits together? explain your reasoning.

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Can someone check my work please? In particularly, part d) -- not sure about this one.

a) 8!
b) (7! x 2)+ (6! x 2)+ (5! x 2) + (4! x 2)
c)8! - [(7! x 2)+ (6! x 2)+ (5! x 2) + (4! x 2)]
d) actually, for me.. part b and c do add up. I think my work for these parts are right though..? so i don't know why they would not add up to the answers in part a. i took the total arrangements and subtracted the times that the partners are together thus i should get the times when they are not together. that's my reasoning, but i'm not sure.

c) how many arrangements are possible if no one is sitting beside his or her partner?

d) explain why the answers from parts b and c do not add up to the answer from part a.

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