TITLE: Drawing cards without replacement: all kings before any jacks
QUESTION [5 upvotes]: This is a question that came up with my friends while playing a card drinking game:
You draw cards without replacement from a standard 52-card shuffled deck. What is the probability that you draw all of the kings before drawing any of the jacks?
I was thinking of a solution along the lines of combinations, but I'm not sure if that's the way to go. Simulation tells me the answer is ~1.4%, but I don't know how to get to this answer.
Disclaimer: This is not a homework question. I'm really just curious.

REPLY [7 votes]: The only thing that matters is the relative placement of the two  critical types of card. 
There are $\binom{8}{4}$ equally likely ways to choose the places occupied by the Kings. Only one of these is "favourable." 
Thus the probability that all the Kings come before any Jack is $\dfrac{1}{\binom{8}{4}}$. This is approximately $0.0143$, quite close to the number obtained in the simulation.