treat each couple as one object. how many ways can you permute these objects to arrange them in a straight line? after you get that, multiply that answer by two, this covers the arrangements where the members of each couple may switch places.

this is the total number of ways we can permute the 8 people, minus the number of arrangements where couples sit together (that is, minus your answer for part (a))b) How many arrangements are possible if no one is sitting beside his or her partner?