16. Arrange $a, b, c, d, e, f$ such that the letter $b$ always appears before the letter $e$. How many such arrangements are there?
16. Divide all permutations of $\{a, b, c, d, e, f\}$ into two categories:
$A=\{x x \cdots x$; where $b$ is before $e$ $\}, B=\{x x \cdots x$; where $b$ is after $e$ $\}$. Clearly, $A \cap B=\varnothing, A \cup B=I,|A \cup B|=6!$.
Define the mapping $f: A \rightarrow B, f(\cdots b \cdots e \cdots)=(\cdots e \cdots b \cdots)$.
$f$ is a one-to-one mapping from $A$ to $B$, $|A|=|B|=\frac{1}{2} \times 6!$.