Aberdeen will host Dundee in the second round of the Scottish Communities League Cup.
There will be a Renfrewshire derby when St Mirren visit Morton, while Clyde entertain Motherwell and Dunfermline make the short trip to East Fife.
Hibernian are at home to Berwick Rangers and St Johnstone welcome Livingston to Perth.
Inverness travel to Ayr United, Hamilton meet Ross County and Falkirk are up against Stenhousemuir.
Airdrie United v Raith Rovers and Queen of the South v Forfar Athletic make up the draw.
Cup holders Rangers enter at the next stage, along with Celtic, Hearts, Dundee United and Kilmarnock.
The draw was held at the Highland Football Academy in Dingwall by MSP Fergus Ewing and Scottish Schools' Football Association president Rod Houston and the area's two Scottish Football League clubs welcomed the draw.
First Division County's manager, Derek Adams, said: "We play Hamilton 10 days before the Cup tie in the league and we're away from home, so it sets up an interesting few days.
"Both sides will feel that they can get through to the next round of the Cup."
Caley Thistle striker Gregory Tade is preparing for a long trip to face First Division outfit Ayr United.
"But, as with all other teams, we'll show them respect and do our best to win and play with our philosophy of working very hard for our team-mates to hopefully get through to the next round."
Scottish Communities League Cup, second round draw:
Hibernian v Berwick Rangers
East Fife v Dunfermline Athletic
St. Johnstone v Livingston
Airdrie United v Raith Rovers
Falkirk v Stenhousemuir
Ayr United v Inverness
Queen of the South v Forfar Athletic
Morton v St. Mirren
Hamilton Academical v Ross County
Clyde v Motherwell
Aberdeen v Dundee