Example 1-7 There are 5 letters $a, b, c, d, e$. Choose 6 to form a string. Requirements: (1) The 1st and 6th must be consonants $b, c, d$; (2) Each string must include the two vowels $a, e$, and $a, e$ must not be adjacent; (3) Adjacent consonants must not be the same. Find the number of strings.
According to the requirements, the two vowels $a, e$ have the following 3 formats: (1) that is, $a, e$ are located at the 2nd and 4th positions, or denoted as $(2,4)$ format; (2) $(2,5)$ format; (3) $(3,5)$ format.
\begin{tabular}{lllllll}
$(2,4):$ & $\bullet$ & $\bigcirc$ & $\bullet$ & $\bigcirc$ & $\bullet$ & $\bullet$ \\
$(2,5):$ & - & $\bigcirc$ & $\bullet$ & $\bullet$ & $\bigcirc$ & $\bullet$ \\
$(3,5):$ & $\bullet$ & $\bullet$ & $\bigcirc$ & $\bullet$ & $\bigcirc$ & $\bullet$
\end{tabular}

where $\bullet$ represents a consonant, $\bigcirc$ represents a vowel. A single consonant has 3 choices, and a pair of consonant characters has only $3 \times 2$ choices.
The $(2,4)$ format has $3 \times 2 \times 3 \times 2 \times 3 \times 2=3^{3} \times 2^{3}$ schemes,
The $(2,5)$ format has $3 \times 2 \times 3 \times 2 \times 2 \times 3=3^{3} \times 2^{3}$ schemes,
The $(3,5)$ format has $3 \times 2 \times 2 \times 3 \times 3 \times 2=3^{3} \times 2^{3}$ schemes.

According to the addition rule, the number of strings $n$ is
$$
n=3 \times 3^{3} \times 2^{3}=3^{4} \times 2^{3}=81 \times 8=648
$$