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Leicester City will travel to League Two Stockport County in the second round of the Carabao Cup, with Newcastle United visiting fourth-tier Tranmere Rovers.
Frank Lampard's Everton have been drawn away to League One Fleetwood Town.
Meanwhile, Steven Gerrard's Aston Villa also face third-tier opposition in Bolton Wanderers.
The second round ties will take place during the week commencing Monday, 22 August.
There are tricky away trips to League Two sides for newly-promoted Premier League Nottingham Forest, who face Grimsby Town, and Fulham, who go to Crawley Town.
A host of top-flight teams will play at League One grounds, with Southampton visiting Cambridge United and Brentford travelling to Colchester United, while Oxford United host Crystal Palace and Forest Green Rovers welcome Brighton.
Elsewhere, Wolves will be at home to Championship side Preston North End, Leeds United host League One Barnsley at Elland Road and Bournemouth visit Norwich City.
Fourteen Championship sides played lower-league opposition in the first round and, after all nine second-tier sides lost matches against lower-ranked clubs on Tuesday, only Blackburn and Rotherham managed to avoid shocks on Wednesday.
Defending champions Liverpool, along with the six other Premier League Clubs who are competing in European competitions this season, will enter the EFL Cup in the third round.
Northern section
Bolton Wanderers v Aston Villa
Derby County v West Bromwich Albion or Sheffield United
Wolverhampton Wanderers v Preston North End
Leeds United v Barnsley
Fleetwood Town v Everton
Sheffield Wednesday v Rochdale
Tranmere Rovers v Newcastle United
Rotherham United v Morecambe
Barrow v Lincoln City
Stockport County v Leicester City
Bradford City v Blackburn Rovers
Grimsby Town v Nottingham Forest
Shrewsbury Town v Burnley
Southern section
Stevenage v Peterborough United
Norwich City v AFC Bournemouth
Newport County v Portsmouth
Oxford United v Crystal Palace
Watford v Milton Keynes Dons
Colchester United v Brentford
Wycombe Wanderers v Bristol City
Walsall v Charlton Athletic
Crawley Town v Fulham
Cambridge United v Southampton
Gillingham v Exeter City
Forest Green Rovers v Brighton & Hove Albion