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Phrase(s): Hobson’s choice
the choice between taking what is offered and getting nothing at all. (From the name of a stable owner in the seventeenth century who always hired out the horse nearest the door.) • We didn’t really want that particular hotel, but it was a case of Hobson’s choice. We booked very late and there was nothing else left. • If you want a yellow car, it’s Hobson’s choice. The garage has only one.
McGrawhill's American Idioms And Phrasal Verbs
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An apparently free choice that actually offers no alternative. For example, My dad said if I wanted the car I could have it tonight or not at all? that's Hobson's choice. This expression alludes to Thomas Hobson of Cambridge, England, who rented horses and allowed each customer to take only the horse nearest the stable door. [Mid-1600s]
American Heritage Idioms