A little probability problem which occurred to me whilst doing my laundry the other day. So far unsolved by a bunch of maths majors, but I'm sure xkcd can do better
I own 7 pairs of socks, one for each day of the week. One pair has 'Monday' on, the second 'Tuesday' etc. I mix them all up in a drawer, and randomly remove 9 individual socks. What is the probability that from the 9 socks I have removed, I can make exactly 2 pairs of matching socks?
There's a trick that makes it easy to solve for this particular case. However I still do not have a solution for the general case of selecting x socks from y pairs and obtaining z matching pairs. Can anyone here provide one?
I sock at maths
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Re: I sock at maths
The general case should be something like [math]\frac{\displaystyle{{y}\choose{z}} {{yz}\choose{x2z}}2^{\displaystyle x2z}}{\displaystyle{{2y}\choose{x}}}[/math]
First we pick which z of the y pairs we take, then which of the remaining yz pairs we take a single sock from, then which single sock to take from each pair.
EDIT: Damn. I nearly didn't notice my 1000th post. I better not have made a mistake now.
First we pick which z of the y pairs we take, then which of the remaining yz pairs we take a single sock from, then which single sock to take from each pair.
EDIT: Damn. I nearly didn't notice my 1000th post. I better not have made a mistake now.
All posts are works in progress. If I posted something within the last hour, chances are I'm still editing it.
Re: I sock at maths
For this particular case, in order to get exactly 2 pair, you need to, at some point, draw at least one of every kind of sock. This makes the calculation pretty easy, but I'm really tired and will let someone else write it.
Re: I sock at maths
There must be a program out there that writes immense treediagrams.
"Woof!", explained the dog

 Posts: 5
 Joined: Sat Feb 14, 2009 3:05 pm UTC
Re: I sock at maths
For those who want the simple
edit: this is the ONLY time I haven't complicated a question
Spoiler:
edit: this is the ONLY time I haven't complicated a question
Re: I sock at maths
xkcdaddict wrote:For those who want the simpleSpoiler:
edit: this is the ONLY time I haven't complicated a question
But the op wanted exactly 2 pairs. Your solution gives at least 2 pairs but possibly as many as 4.

 Posts: 5
 Joined: Sat Feb 14, 2009 3:05 pm UTC
Re: I sock at maths
Sorry, I misread the question as "guaranteed to have exactly 2 pairs."
English + late night != good
I agree with Token btw.
English + late night != good
I agree with Token btw.
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