TITLE: What is the probability that at least 10 cards go by before the first jack?
QUESTION [0 upvotes]: Suppose we keep dealing cards from an ordinary 52-card deck until the first jack
appears. What is the probability that at least 10 cards go by before the first jack?

The outcome space is ${52\choose10}$ Since you choosing $10$ spots from $52$ cards. Now how do I determine the probability that at least 10 card by by before the first jack?  
There are 4 jacks in a 52 card deck. Pretty sure I have to figure out how many ways can I select 10 cards that are not jacks at the top. Unsure how do I go about this visually.

REPLY [2 votes]: The probability that the first card is not a Jack is 48/52. If this happens, the probability that the second card is not a Jack either is 47/51. The probability that none of the first ten are Jacks is 
$$\frac{48.47.46\ldots 39}{52.51.50\ldots 43}$$
$$=\frac{48!42!}{38!52!}=0.4134453782$$
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