The number of ways of arranging the letters AAAAA BBB CCC D EEF in a row if the C are  separated from one another is_______

First arrange other letters AAAAA BBB DEEF in  $\frac{12!}{5!3!2!}$ way's now insert 3 c’s in the gaps between the letters This can be done is  $\frac{{13}_{P_3}}{3!}=\frac{13!}{10!3!}$ ways