PUZZLE 071 Password ABCs

Now what was the password to the safe?
It's six letters long, and uses the letters 'A', 'B', and 'C'.
Use the pointers on the memo to figure out the correct password and open the safe.
1. The same letter is repeated twice in a row in two different places.
2. The same letter never appears three times or more in a row.
3. The letters 'A' and 'C' appear with the same frequency, which is less than the frequency of letter 'B'.
4. After a 'C', there is always an 'A'.

Hint 1

Look at this hint: the letters 'A' and 'C' appear with the same frequency, which is less than the frequency of letter 'B'.
Use this to work out the possible number of times each letter could appear.

Hint 2

Continuing on from hint one...
The frequency of the letters could be as follows:
A: 0, B: 6, C: 0
or
A: 1, B: 4, C:1

Hint 3

We know from the memo that there are no letters that are unused, so that means the frequency of the letters is A: 1, B: 4, C: 1.
Now you need to put the letters together in pairs.

Super Hint

Putting the letters in pairs gives us three groups: BB, BB and CA.
Now you just need to put them in an order that avoids having three or more of the same letter in a row, and you have your password.

Answer for 'Password ABCs'

The answer is 'BBCABB'.