3) Eight people (four couples) are attending a dinner. One of the four couples is hosting the dinner. The people are sitting at a rectangular table with 3 people along each long side and one person on each short side. The seats are numbered from 1 to 8 as shown. 2 6 5 a) How many different ways can the people be seated? b) How many different ways can the people be seated if the host couple must occupy the two seats on the short sides (the head and the foot) of the table? c) How many different ways can the people be seated if every couple must be seated directly across from one another? d) How many different ways can the people be seated if every couple must be seated directly across from one another and the host couple must occupy the two seats on the short sides of the table? e) If every couple leaves together and the host couple does not leave (because they are already home), then how many different possible orders of couples leaving exist