Checking some Regular Expression problems I'm given the alphabet $$ \Sigma = {\{a,b}\} $$ 
I tried to write a regular expressions for presenting the following sets:
All strings in $$\Sigma ^ *$$
 with:
a-) number of 2s divisible by 4
b-) exactly one occurrence of 122
c-) exactly one or two 1s
Well I tried to find their solutions, but I am afraid they might be incomplete. So it goes like:
$$ (1^*(22)^*1^*)^* $$ 
$$ 2^*1222^* $$ 
$$ 2^*(1 | 11)2^* $$ 
respectively for a, b and c parts.

a). Words with number of $2$s divisible by 4 are words made of subwords that contain exactly 4 $2$s with arbitrary number of $1$s between them.
$$(1^*21^*21^*21^*21^*)^*$$
b). Note that $(21^*+11(1+2)+121)^*$ is the complementary of $122$.
$$(21^*+11(1+2)+121)^*122(21^*+11(1+2)+121)^*$$
c). In a similar concept as in case (a),
$$2^*12^*+2^*12^*12^*$$
