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Bill has a small deck...

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JOHN.T.SNIPES
 Post subject: Bill has a small deck...
 Post Posted: Thu Oct 06, 2011 2:30 pm 
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Posts: 5
Can someone show me how to solve this problem using factorials?

Quote:
Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, for each value from 1 to 6, there are two cards in the deck with that value. Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
8/33
62/165
17/33
103/165
25/33


I seem to be struggling w combination problems largely in deciding what the best method of answering the question is and how to proceed (which is probably a product of my lack of understanding combination stuff in general). In retrospect I see that it makes sense to use the 'slot method' and to also find the probability of there NOT being any pairs. So basically:
(12/12)*(10/11)*(8/10)*(6/9)=16/33 and 1-16/33= 17/33 or C.

But I feel like I should be able to get to this same answer using some combination of x!/(x-n)!n! or something. Appreciate any help.
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JOHN.T.SNIPES
 Post subject: Re: Bill has a small deck...
 Post Posted: Sun Oct 09, 2011 11:59 am 
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Posts: 5
anyone? bueller?
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700+
 Post subject: Re: Bill has a small deck...
 Post Posted: Tue Oct 11, 2011 7:36 pm 
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Students


Posts: 23
Location: Bangalore
I would like to inform you that, this question has already been answered few times. I'm sure all your doubts would be cleared. Here are the links

http://www.manhattangmat.com/forums/bill-has-a-small-deck-of-12-playing-cards-t1898.html

http://www.manhattangmat.com/forums/a-beautiful-pair-t6176.html

http://www.manhattangmat.com/forums/viewtopic.php?f=32&t=11107&view=next

http://www.manhattangmat.com/forums/combinatoricsprobability-ron-stacey-help-pz-t5651.html
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jnelson0612
 Post subject: Re: Bill has a small deck...
 Post Posted: Sun Nov 20, 2011 12:06 am 
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ManhattanGMAT Staff


Posts: 1857
Thanks 700+!

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Jamie Nelson
ManhattanGMAT Instructor
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