ex1. I'm bored - there's nothing to do (= There are no entertainment)
ex2. There's nothing to be done - we'll have to buy a new one (= There's no way of putting it right)
I can understand ex1, but I can't ex2. What does ex2 mean? What does 'nothing to be done' exactly mean?
"nothing to be done" means, roughly, "nothing that can be done". The thing that would "be done", if it existed, is the remedy to fix whatever problem or difficulty is being referred to. Another example of the same pattern is "There was nothing to be said".
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"nothing to be done" means, roughly, "nothing that can be done". The thing that would "be done", if it existed, is the remedy to fix whatever problem or difficulty is being referred to. Another example of the same pattern is "There was nothing to be said". In my opinion it is not fully predictable that "nothing to do" and "nothing to be done" have the contrasting meanings that you describe. Yo