Concept:
Sentence arrangement requires identifying the grammatically and logically correct order of phrases.
Step 1: Identify the introductory phrase.
The sentence starts with:
\[
\text{Scarcely had we}
\]
Thus:
\[
C \rightarrow \text{First}
\]
Step 2: Find the next meaningful phrase.
After this, the phrase:
\[
\text{reached the office}
\]
fits naturally.
Thus:
\[
B \rightarrow \text{Second}
\]
Step 3: Add the conjunction clause.
The next suitable phrase is:
\[
\text{when it}
\]
Thus:
\[
D \rightarrow \text{Third}
\]
Step 4: Complete the sentence.
The remaining phrases are:
\[
\text{started raining}
\]
and
\[
\text{cats and dogs}
\]
Thus:
\[
A \rightarrow \text{Fourth}
\]
\[
E \rightarrow \text{Fifth}
\]
Step 5: Write the complete sentence.
\[
\text{Scarcely had we reached the office when it started raining cats and dogs.}
\]
Step 6: Conclusion.
Hence, the correct arrangement is:
\[
\boxed{C,\; B,\; D,\; A,\; E}
\]