League Cup holders Celtic will play Ross County in the first match of their defence of the trophy.
The draw took place after Hibernian had beaten Dundee 4-1 in the last of the group stage games on Sunday, with three all-Premiership ties in the first of the knockout rounds.
St Mirren will host Aberdeen, while Motherwell are at home to St Johnstone.
Premiership leaders Rangers travel to play Falkirk, while Livingston have a home game against Ayr United.
After their group stage game at Easter Road on Sunday, the draw put Hibs and Dundee together again at the same venue in the second round.
Arbroath are at home to Dunfermline and Alloa will welcome Hearts.
Aberdeen, Celtic, Dunfermline, Hearts, Hibs, Livingston, Motherwell and Rangers were the seeds in the draw as the SPFL’s European representatives and the four teams with the best record from the group stage.
Second round ties will be played on the weekend of November 28.
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