Is my dataset too small for what I want to do? (multi-categorization)

I'm working with a dataset of about 200,000 jeopardy questions, and I'd like to use NLP to categorize them into broad categories (history, math, sports, etc).

From doing a cursory check of how many history questions I have (just checking if 'histor' appears in the category) I have about 450 history questions. Obviously there are more that don't have that string in the category, but it would take a fair bit of manual work to identify those.

Given that, and …

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