The possible seating arrangements would be 5! or 5P5 since this is a permutation. Since order matters here you can place 5 people in the first seat, that leaves 4 people left for the second seat, 3 people left for the third seat, 2 people for the fourth seat, and 1 person left for the fifth seat. So the answer is 120 different seating arrangements for these 5 people. If A and B must sit next to each other, you treat them as one person, so instead of having 5 people to choose from, you essentially have "4" people to choose from, (since A and B now count as one person.) So your answer to this would be 4! or 4P4, which equals 24 different ways.
