# probability Theory

I need an explanation on the following problem:

If you are dealt $3$ cards from a shuffled deck of $52$ cards, find the probability that all $3$ cards are picture cards.

I found the total number of possible combinations, $\binom{52}3=22100$. now my books uses $\binom{12}3$ to find the number of ways to select $3$ picture cards, which is $220$.

My question is where does the $12$ come from? Why $12$ and not $16$ (number of picture cards on the deck of $52$)?

Thank you

Jorge

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There are 12 "picture cards", kings, queens, and jacks. An Ace isn't a picture I suppose. –  David Mitra May 13 '12 at 18:39
Aces don't count. –  Double AA May 13 '12 at 18:40
Thank you, it really makes sense now, I was counting the Ace as a picture card. –  Jorge Reis May 13 '12 at 18:54
Someone voted to close this as off-topic? Sorry, I don't understand the reasoning there. –  Gerry Myerson May 14 '12 at 6:09