Construct a DFA without e$-$transition for the set of strings over $\{$a$,$b$,$c$\}$ in which there is at least one c if the strings$$ length are at least $3.$

A$.$

There is a solution DFA that has $3$ states including $3$ final states.

B$.$

There is a solution DFA that has $4$ states including $4$ final states.

C$.$

There is a solution DFA that has $4$ states including $3$ final states.

D$.$

There is a solution DFA that has $5$ states including $5$ final states.

E$.$

There is a solution DFA that has $5$ states including $4$ final states.