
As far as I understand, "what choices do I have?" and "what choice do I have?" are different. The former is asking about the options I have, and the latter is a rhetorical question, e.g. "I don't want to do this, but what choice do I have?", that is to say I have no choice (if we treat "choice" as an uncountable noun meaning "the ability to choose") or only one choice (if we treat "choice" as a countable noun synonymous with "option"). Either way, the singular fits this meaning perfectly.
(Replace "I" with "you" etc.)

Thanks.
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