Aberdeen's visit to Falkirk in the will be broadcast live on BBC TV.
The match on Wednesday 25 September has a 19.15 kick-off and will be shown on BBC Two Scotland.
at home in the previous round.
Aberdeen needed penalties to dispose of Falkirk's Championship rivals, Alloa Athletic, .
The Dons and Falkirk were last in opposition in October 2010, when Aberdeen won 2-1 at home in the League Cup.
Aberdeen suffered a defeat on their last visit to Falkirk Stadium, losing 3-1 in February 2010 in the Scottish Premier League.
The Bairns are unbeaten in their previous three home games against the Dons, who last won there in October 2008, 1-0 in the league.
Aberdeen's last three League Cup visits to Falkirk have all ended in 4-1 victories for the Dons.
Meanwhile, the latest Scottish Premiership match to be broadcast "as live" on BBC Alba will be Saturday's meeting between Aberdeen and St Johnstone.
The full match, which kicks off at 15:00 at Pittodrie, will be shown from 17:30.