"What would have been your chances?" vs "What would your chances have been?"
Which one is grammatically correct and why?
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Some general recommendations in English prose syntax are to avoid separating a subject from its predicate, and to avoid interposing adverbs, objects, or other words into a predicate with multiple parts. Your predicate is "would have been", which we'd want to keep together whenever possible. Of course, as with all such "rules", writers can choose to except them with cause. As far as meaning, I don't see much difference.