If Man Utd get a draw against Bournemouth and Crystal Palace win the FA Cup final, the European participants will be as follows:
Champions League: Leicester City, Arsenal and Tottenham
Champions League qualifiers: Manchester City.
Europa League: Crystal Palace, Man Utd
Europa League qualifiers: Southampton
Unless I'm calculating incorrectly, Leicester City will be in pot 1, Arsenal (and Man City if they qualify) in pot 2 and Tottenham in pot 3.
Southampton in the Europa League qualifiers could prove to be tricky for the Premier League.
Other possible options:
- Man Utd lose against Bournemouth, Crystal Palace win FA Cup: Crystal Palace and Southampton in Europa League group stage, Man Utd in EL qualifiers
- Man Utd win FA Cup: Man Utd and Southampton in Europa League group stage, West Ham in EL qualifiers