$(5$ points$)$ Section $1\mathrm{.}2$ Question $14($Grammars$)$:

Find grammars for $=\{$a$,$b$\}$ that generate the sets of

$($a$)$ all strings with exactly two a$\text{'}$s$.$

$($b$)$ all strings with at least two a$\text{'}$s$.$

$($c$)$ all strings with no more than three a$\text{'}$s$.$