From Longman Dictionary of Contemporary EnglishHobson's choiceHob‧son’s choice /ˌhɒbsənz ˈtʃɔɪs $ ˌhɑːb-/ noun [uncountable] CHOOSEa situation in which there is only one thing you can do, so you do not really have any choice at all
Examples from the Corpus
Hobson's choice• But, in terms of disability services, the choice available to us amounts to little more than Hobson's choice.Origin Hobson's choice (1600-1700) Probably from Thomas Hobson (1554-1631), who rented out horses and would only let his customers take the horse nearest the door 