Which sentence below is properly punctuated?
a.
bertie had several people working for him; a private secretary, an administrative assistant, and a research aide.
b.
bertie had several people working for him, a private secretary, an administrative assistant, and a research aide.
c.
bertie had several people working for him: a private secretary, an administrative assistant, and a research aide

Option C is correctly punctuation. The colon is used because you're listing off the different types of employees Bertie has working for him. The types of a people are dependent clauses (that is, by themselves, they don't make a completely sentence). Had there been a bridging word or phrase like "including" or "for example" then you wouldn't need a colon because those words would serve the same function. A semicolon does not work in this case because that would be used to connect two independent clauses without a conjunction between them (i.e. "and", "or", "but" etc.).

Nope but maybe you should study