You decide to have a dinner party. You have 15 different friends but you only have enough chairs to invite 7 of them. Find the number of ways your 7 invited friends can sit in a row where two of your friends insist on sitting next to each other. How many choices do you have for which 7 friends to invite? What if you need to decide not only which friends to invite but also where to seat them along your long table? How many choices do you have then? Find the number of ways your 7 invited friends can sit around a circular table where two of your friends A and B must not sit next to each other