$a$, $b$ and $c$ are distinct digits,
$$\begin{aligned}
& a \cdot b < 8 \\
& a \cdot c > 10 \\
& b \cdot c = 12
\end{aligned}$$
Given these statements.
Accordingly, what is the sum $\mathbf{a} + \mathbf{b} + \mathbf{c}$?
A) 9
B) 11
C) 13
D) 15
E) 17