I think the answer is (13c₃)(12!/5!3!2!)

First,arrange All A's,B's,D,E's,F in a row in 12!/5!3!2! ways.There are 11 gaps in between and 2 at the end.Select 3 of these 13 gaps and fill them up with C's in 13c₃ ways.Hence,the answer is 13c₃.[12!/5!3!2!].