TITLE: Find the probability that the card number 18 is the second jack that you deal.
QUESTION [7 upvotes]: You deal from a well-shuffled $52$-card deck, one card at a time. Find the probability that the card number 18 is the second jack that you deal. Include at least $4$ digits after the decimal point in your answer.

I have tried this numerous different ways, but I cant seem to get it. 
I've tried 
$$\frac{\dbinom{48}{16} \cdot \dfrac{4}{52}}{\dbinom{52}{16} \cdot \dfrac{3}{35}}$$ 
and I don't know why this doesn't work.

REPLY [2 votes]: The first $17$ cards can be a single jack ($1$ from $4$) plus any $16$ from $48$. The $18$th card can be one of $3$ jacks from the $35$ remaining cards. So I get: $$4\cdot \frac{\binom{48}{16}}{\binom{52}{17}}\cdot \frac{3}{35} = 0.03523$$