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The two sides have only met once before in the competition - back in 1979 when the Millers pulled off a shock 0-0 draw at Maine Road.
City then travelled to Millmoor for the replay and won 4-2.
The teams have only met 11 times competitively, with City yet to suffer defeat.
📺⚽ Third Round TV Picks— The Emirates FA Cup (@EmiratesFACup) December 6, 2018
Who will you be watching? 👀 pic.twitter.com/5kG7N6z5qD