FA Cup

The FA Cup winners qualify for the following season's UEFA Europa League (formerly named the UEFA Cup; from its launch in 1960 until 1998, they entered the now-defunct UEFA Cup Winners' Cup instead). This European place applies even if the team is relegated or is not in the English top flight. In the past, if the FA Cup winning team also qualified for the following season's Champions League or Europa League through their league position, then the losing FA Cup finalist were given this European berth instead. FA Cup winners enter the Europa League at the group stage. Losing finalists, if they haven't qualified for Europe via the league, began earlier, at the play-off or third qualifying round stage. From the 2015--16 UEFA Europa League season, however, UEFA does not allow the runners-up to qualify for the Europa League through the competition. If the winner -- and until 2015, the runner-up -- has already qualified for Europe through their league position (with the exception of the UEFA Cup until 1998), the FA Cup berth is then given to the highest-place team in the league who has not yet qualified.

Question: do the fa cup runners up qualify for europe
Answer: no