$$\begin{aligned}
& a = 5 ! \cdot 9 ! \\
& b = 6 ! \cdot 8 ! \\
& c = 7 ! \cdot 7 !
\end{aligned}$$ Given that, which of the following orderings is correct? A) $a < b < c$ B) $a < c < b$ C) $b < c < a$ D) $c < a < b$ E) $c < b < a$
$$\begin{aligned}
& a = 5 ! \cdot 9 ! \\
& b = 6 ! \cdot 8 ! \\
& c = 7 ! \cdot 7 !
\end{aligned}$$
Given that, which of the following orderings is correct?
A) $a < b < c$
B) $a < c < b$
C) $b < c < a$
D) $c < a < b$
E) $c < b < a$