Palace have won their last three games against the Cherries, scoring eight goals and keeping two clean sheets in the process - most recently a 2-0 win in the club's first post-lockdown Premier League fixture back in June.
The tie against Jason Tindall's side will be the first time Bournemouth and Palace have ever met in a cup competition.
Whoever advances to Round Three will face Carabao Cup holders Manchester City the following week on either 22nd or 23rd.
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