Manchester United defeated Chelsea 2-1, while Liverpool won 5-4 on penalties against Arsenal on Wednesday.
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Manchester United will host Colchester Utd in the Carabao Cup quarter-final clash.
The draws were conducted on Thursday morning, following the conclusion of the round of 16 fixtures on Wednesday night. Manchester United defeated Chelsea 2-1, while Liverpool won 5-4 on penalties against Arsenal on Wednesday.
Fixtures for the quarter-finals will commence on December 16.