After having trained dozens of trading classes at Fidelity, I came to the conclusion that they would hire just about anyone, lol. I'm sure most discount brokers are pretty similar.
A typical entry level position at any brokerage firm would be the Customer Service Representative. Some companies would prefer that you already have a Series-7 and Series-63 licenses, while others (like Fidelity) are willing to hire you and train you in preparation for getting your licenses.
I can also tell you that you I've been on both sides of the phone, and I'd much rather be on this one, lol!
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