Concept:
After modal verbs such as
\[
may,\ can,\ should,\ must,\ will
\]
we use the base form of the verb.
So after
\[
may
\]
we should use
\[
have
\]
not
\[
having
\]
Step 1: Identify the mistake.
The phrase is:
\[
\text{may having}
\]
This is incorrect.
Step 2: Correct the phrase.
The correct phrase is:
\[
\text{may have}
\]
Step 3: Correct sentence.
\[
\text{Some students may have many books with them.}
\]
So the mistake is in part \(2\).
Step 4: Final answer.
\[
\boxed{2}
\]