phrase structure grammar

[logistic_guy]

here is the question

Find a phrase-structure grammar that generates each of these languages.

(a) The set of bit strings of the form $\displaystyle 0^{2n}1^{3n}$, where $\displaystyle n$ is a nonnegative integer.
(b) The set of bit strings with twice as many $\displaystyle 0$s as $\displaystyle 1$s.
(c) The set of bit strings of the form $\displaystyle w^2$, where $\displaystyle w$ is a bit string.


my attemb
i'll start with (b) because i think it's easy
let me start with simple string $\displaystyle 001$
i think changinging the order is allowed so we've another string $\displaystyle 100$
i'm not sure if the zeros not stick together is a correct string like $\displaystyle 010$
now i've to change the digits with letters
$\displaystyle A = 0$
$\displaystyle B = 1$
if $\displaystyle S$ the start state, then my string has the form $\displaystyle AABS$
i'm not sure about the case $\displaystyle ABAS$, so i'm not certain if $\displaystyle A$ and $\displaystyle B$ can be written in any sequence
so my production step $\displaystyle P$
$\displaystyle S \to AABS$
if i'm allowed to change the order, then i've another production step
$\displaystyle AAB \to BAA$
$\displaystyle BAA \to AAB$
so my phrase-structure grammar
$\displaystyle G = \{V,T,S,P\}$: set of all letters i use
$\displaystyle V = \{0,1,A,B,S\}$: set of all alphabets i use
$\displaystyle T = \{0,1\}$: set of all digits i use
$\displaystyle S \to AABS$
$\displaystyle AAB \to BAA$
$\displaystyle BAA \to AAB$
$\displaystyle A \to 0$
$\displaystyle B \to 1$

is my solution and analize correct?