A committee with $20$ members votes for the candidates $A,B,C$ by a different election system. Each member writes his ordered prefer list to the ballot (e.g. if he writes $BAC$, he prefers $B$ to $A$ and $C$, and prefers $A$ to $C$). After the ballots are counted, it is recognized that each of the six different permutations of three candidates appears in at least one ballot, and $11$ members prefer $A$ to $B$, $12$ members prefer $C$ to $A$, $14$ members prefer $B$ to $C$. How many members are there such that $B$ is the first choice of them? 

$ \textbf{(A)}\ 5
\qquad\textbf{(B)}\ 7
\qquad\textbf{(C)}\ 8
\qquad\textbf{(D)}\ 10
\qquad\textbf{(E)}\ \text{More information is needed}
$