high school diploma and GED?

YES!

A GED is designed to be a substitute for a high school diploma. If you have a diploma from an accredited school, there is no reason to get a GED. Having both a diploma and a GED would probably just raise questions about your high school education, which might actually hurt your chances.

If your school is not accredited, or you are not based in the same country as the university you're applying for, you might consider it, but even then, the best thing you can do is this: Ask the universities! The admissions councilor's job is to answer your questions, and nobody expects you to already know the answers to this kind of thing, so they won't count these questions against you.

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The more high school experience you have the better. I suggest at least seven years.