# Probability of getting 4 aces while drawing 6 cards.

Drawing 6 cards from a standard deck of 52 cards, what is the probability of getting 4 aces?

This answer explains how to calculate the odds of a getting any 4-of-a-kind in a 5-card draw. I was hoping it would be obvious how to adjust that solution to solve my problem, but I'm not confident that I understand it well enough.

Given that there are 13 possible 4-of-a-kinds, and I am concerned with only 1 of them, I would assume the odds are 13 times less likely than simply drawing a 4-of-a-kind, but that's where I run out of steam.

$$\frac{{4\choose4}{48\choose 2}}{52\choose6}$$
Note this is $$\frac1{13}$$ of the (fairly easy) adaptation from your link to $$6$$ choices.
• The two answers match. I checked it. I adjusted the solution for the fact that $6$ choices are made rather than $5$. – Chris Custer Oct 1 '18 at 14:35