I am trying to solve the puzzle below and am thinking that there ought to be some way of formulating it as a problem about counting matchings, but I can not make it work. I would appreciate a hint or a different strategy.
N premier league footballers, all with different birth dates, and a single female, Natasha, are to be seated at a round table. To avoid any footballers getting ignored, each footballer must either sit next to a younger footballer or to Natasha. In how many ways can the footballers and Natasha be seated?