Find all $12-$letter strings that use the letters from $\{A,B,C\},$ where two strings are considered the same if one is obtained from the other by rotations, in each of the following cases.

$($a$)$ all strings,

$4$ letterstring using $2$ letter $\{A,B\}$

$($b$)$ only strings that contain at least one of each letter, $\frac{?}{{?}_{\frac{?}{?}}\text{B}\text{B}\text{A}}$ AAAB $\frac{?}{{?}_{\frac{?}{?}}\text{A}\text{A}\text{A}\text{c}\text{d}\text{o}\text{t}\text{s}2}*2*2*2=2^4$

$($c$)$ strings that contain at least one letter $A,$

$($d$)$ strings that contain six $A$ s$,$ three $Bs,$ and three $Cs,$

$($e$)$ strings that contain $4$ of each letter.