How to delete an answer choice as people choose them

I am trying to schedule people for shifts, and i need a way so that when someone who is taking the survey chooses an answer choice from the drop down menu, and they submit their responses, that answer choice will not appear for the next person who takes the survey. Currently I have it set up as a multiple choice question with a drop down menu consisting of 9 options for the same shift. I would like it to be such that if someone chooses one of those options, it will remove that option from the question for the next person. This is so I can limit the number of people working on the same shift.