I tried this before an got in a mess. This time I am more confident.
But there is still plenty of room for error.
Seat each person and tie their chair to the chair on the right (which will be empty.)
Think of the 2 chairs and the one person as a single unit.
So now you have 3 fat units and 12 more chairs.
You have to slip the fat units between the other chairs.
15 units altogther and you need to choose the 3 that are fat.
so that is 15C3= 455
Now the three people can be in any order so that is 3!=6 ways
455*6=2730 ways