Holders Celtic have been drawn away to Hearts in the fourth round of the Scottish Cup.
The tie was one of four all-Scottish Premiership encounters picked out of the hat as Alex Ferguson helped conduct the draw in Aberdeen.
In the others, Dundee United will host Kilmarnock, Hibernian travel to Dingwall to face Ross County and Ferguson’s former club, Aberdeen, will play Partick Thistle at Firhill.
Two of the clubs the former Manchester United manager played for, Falkirk and Rangers, were first out of the hat and will play at the Falkirk Stadium.
Elsewhere, Inverness host Morton, St Johnstone are at home to Livingston and St Mirren get the chance to avenge their League Cup defeat by Queen of the South when they return to Dumfries.
Motherwell make the short journey to Coatbridge to face Lanarkshire neighbours Albion Rovers while there are other local derbies between Brechin and Forfar, and Alloa and Stirling.
Rangers take on Dunfermline on Wednesday in Scottish League One. Rangers’ Nicky Clark said the match will have a top-flight feel to it as it’s only 21 months since the clubs last played in a competitive game in the SPL.
Since then the Pars have gone through two relegations — one because of administration — and the Gers moved down to SFL3.
Clark said: “We’ve both been in the SPL recently and they’ll be looking forward to coming to play at Ibrox.”