Решение:
Выбираем модальные глаголы, соответствующие ситуации:
- can't (нельзя, запрещено) — eating in the classroom is not allowed.
- don't have to (нет необходимости) — cleaners will do it, so students don't need to take rubbish out.
- can't (нельзя, невозможно) — the entrance is closed.
Ответ: can't, don't have to, can't.