Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

share|improve this question
6  
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
1  
Someone voted to close this as off-topic? Sorry, I don't understand the reasoning there. –  Gerry Myerson May 14 '12 at 6:09

2 Answers 2

This is a matter of semantics. What is a "picture card"? I surmise the book thinks it's the queens, kings, and jacks (giving twelve); but not the aces (but not sixteen).

On the other hand, I would consider many of these aces to be picture cards. So your interpretation that there are sixteen picture cards might be justified. I suppose it depends on your experience with playing cards. In any case, in my opinion, the problem is slightly vague.

If in doubt of what some particular phrase means in a problem, it would be a good idea to state what your assumptions are in your write up of a solution. Here, if you were adamant in your stance that aces were picture cards, I would say "I take as the picture cards, the queens, kings, jacks, and aces".

share|improve this answer

lolz actually picture cards refer to cards which have picture : Jack,queen, King so 4 suits: 4x3=12 ace don't count generally ace don't have picture.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.