Holders Celtic have been drawn at home to Raith Rovers in the third round of the League Cup.
In the ballot, which took place at Hampden Park, Aberdeen were drawn away against Hibs while St Johnstone travel to play the latest Ibrox club.
Gary Locke will return to former club Hearts with Kilmarnock while Scottish Cup winners Inverness Caley Thistle face Livingston at Almondvale.
Dunfermline’s reward for knocking out Paul Hartley’s Premiership outfit Dundee in the second round is a trip to Dundee United and Morton have been paired with Motherwell, who needed extra-time to beat East Fife to reach this stage.
Kilmarnock v Hearts
Livingston v Inverness CT
Ross County v Falkirk
Celtic v Raith Rovers
Morton v Motherwell
Dundee United v Dunfermline
Hibernian v Aberdeen