Let $S$ denote the set of all languages $L$ over the alphabet $=\{0,1\}$ which only contain strings of length

exactly $4.($The languages in $S$ may contain all the strings of length $4,$ just some of them, or no strings at all!$)$

$($a$)$ How many languages are in $S?$ Give an explanation or proof for your answer.

$($b$)$ Prove that every language in $S$ has a DFA that recognizes it$.$

$($c$)($BONUS$,10$ additional points$)$ For each LinS, let $s(L)$ denote the minimum number of states needed by a DFA that recognizes $L.$ What is the maximum, over all LinS, of $s(L)?$ Prove your answer.