One might complicate things by thinking of this question as on of combination problems. It can be solved in a lot easier way as follows:
The list of alphabets = {A,B,B,C,C,C}
From this list, we are to choose 5 alphabets. If you look closely, you will know that there are three ways of doing this:
1. You could pick both B's and all C's, {B,B,C,C,C}
In this case, the arrangements possible are 5!/(2!x3!) = 10
2. You could pick the single A, one of the B's and all C's, {A,B,C,C,C}
In this case, the arrangements possible are 5!/(3!) = 20
3. Lastly, you could pick the single A, both B's and two of the three C's,{A,B,B,C,C}
In which case, the arrangments possible are 5!/(2!x2!) = 30
Hence, the correct answer choices are B, D, and F