I have a 60 card deck (MTG) that can contain up to 4 of the same cards. What is the probability that I will select 4 of the same cards within 17 successive draws. Assume, cards are removed and not replaced. Nothing else happens to the deck outside of the draw.

At first I started with (4/60)*(3/59).... This seemed to be a best case scenario.

I moved to n=1,17. (4/60-n)*(3/59-n)... However, this didn't seem to fit but I can't put my finger on it. Outside that doesn't seem to account for number of draws when a failure state happens.

Next I considered I am only working with 17 cards. Of which I have 4/60+1/17 of even 1 of them being the card I need. .066*(4/17)*(3/17)... Still not accounting for the success/fail at any point.

I am sure I am over simplifying the issue. What terms/formulas should I be looking for to express this problem? Thank you for any assistance.

Irons.