In my textbook it says that there is no statement you could deduce from the above two statements in the title. However in my opinion it would be possible to deduce "Some C are no A" from it.
$$ (\forall B \rightarrow \neg A) \wedge (\exists C \rightarrow B) \Vdash (\exists C \rightarrow \neg A) $$
Intuitively this would make sense for me and I also did a quick proof with tableau calculus. Now I am not sure if there is an error in my textbook or if I'm missing something. Either I wrongly converted the statements into boolean logic or the entailment is in fact not true.