How good is your math?
What you’re looking for is Hypergeometric Distribution. I’m sure there are calculators online. I know you have roughly a 25% chance to draw any given 3-of in a 49 card deck. You can toy around with it to figure math in 49 vs 54 card decks, and for 1-ofs and 2-ofs. If you know how to do factorials (or punch them in somewhere) the math isn’t too difficult. The Wikipedia article is highly informative.