Construct a Deterministic Finite Automaton $($DFA$)$ for each of the following languages:

a$)$ The set of all strings over $\{a,b,c\}$ that end with $bb$ and contain at least one $a.($For example, acbaabb and abb are in the language, but bbac and $bb$ are not in the language.$)$

b$)$ The set of all strings over $\{a,b,c\}$ that do not contain $abc$ as a substring. $($For example, abac,cba, and $bb$ are in the language, but abca and bccabcb are not in the language.$)$