# Card probability - AAKK out of a deck
**URL:** https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241
**Category:** Factual Questions
**Created:** [December 22, 2004, 11:21pm UTC](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241 "2004-12-22T23:21:24Z")
**Posts on this page:** 5
**Page:** 2
### Author:  [@bitwise](https://boards.straightdope.com/u/bitwise)
#### Post date: [December 23, 2004, 5:05am UTC](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241/21 "2004-12-23T05:05:21Z")
> [@ultrafilter](#):
>
> Ask any mathematician how hard counting is, and he’ll tell you it’s frightfully difficult. That’s not widely known outside of our circle, so I can see where somebody might take offense, but none was meant.
>
> Anyway, **bitwise** is using a generalized form of the hypergeometric distribution, which might be of interest to you. It makes problems like this quite simple.
I was? I vaguely remember that there was something called the hypergeometric distribution. It’s been a long time since I took probability. I explained my reasoning using counting methods above.
What is the generalized hypergeometric distribution? I found this
[http://mathworld.wolfram.com/HypergeometricDistribution.html](http://mathworld.wolfram.com/HypergeometricDistribution.html)
and this
[http://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html](http://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html)
I can sort of see how you can generalize the hypergeometric distribution to a multivariate distribution. I have no idea how the second link is related.
---
### Author:  [@nivlac](https://boards.straightdope.com/u/nivlac)
#### Post date: [December 23, 2004, 9:25am UTC](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241/22 "2004-12-23T09:25:12Z")
> [@Pullet](#):
>
> Then **nivlac** phrased it poorly.
>
> That’s all. I don’t mean to pick a fight with anyone and I probably just over-reacted in my previous post.
>
> Don’t want to hyjack the thread.
Yes, absolutely no insult of any kind intended in my original post. And I’m glad that fellow Dopers have jumped to my defense. When I teach this stuff (combinatorics), I always introduce the subject by saying that we will now learn how to count. The title of the chapter in the textbook is “counting techniques”. Then I go into examples to illustrate how difficult it is to count. Remember that probabilities are based on relative frequencies which is just a fancy way of saying dividing one count by another count. In the original question involving the probability of getting 2 aces and 2 kings when 4 cards are dealt from a 52 deck card, the answer is the ratio of the number of ways of getting 2 aces and 2 kings divided by the number of ways of getting 4-card hands. So you have know how to count to get the correct numerator and the denominator. Knowing combinatorics helps, but there are ways to reason it out as **neuroman** did.
---
### Author:  [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)
#### Post date: [December 23, 2004, 4:43pm UTC](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241/23 "2004-12-23T16:43:26Z")
> [@ultrafilter](#):
>
> Ask any mathematician how hard counting is, and he’ll tell you it’s frightfully difficult.
Okay, now I’m wondering:
Does The Count from Sesame Street know about permutations and combinations and all those complexities but he dumbs it down for the kiddies, or is he really not as great a count-er as he pretends to be?
---
### Author:  [@Pullet](https://boards.straightdope.com/u/Pullet)
#### Post date: [December 23, 2004, 5:33pm UTC](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241/24 "2004-12-23T17:33:10Z")
My appologies, **nivlac** , for being quick-tempered, but I’m glad y’all can see how I might take exception. Like I said before, I only know enough math to know I don’t know much, so I couldn’t appreciate the non-offensive qualities of your previous post.
Now that I’ve got my emotions under control, let’s get back to serious discussion.
The Count has, and always will be, a charlatan. A finishing school drop-out, the Count has had to build a career out of the one thing he did manage to learn, combinatorics. That, and he’s a jerk. He laughs everytime he’s counting because he realizes just how much he’s screwing up the little kiddie’s future math studies.
---
### Author:  [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)
#### Post date: [December 23, 2004, 6:03pm UTC](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241/25 "2004-12-23T18:03:35Z")
> [@Thudlow Boink](#):
>
> Okay, now I’m wondering:
> Does The Count from Sesame Street know about permutations and combinations and all those complexities but he dumbs it down for the kiddies, or is he really not as great a count-er as he pretends to be?
The Count is quite clearly a master of enumerative combinatorics.
[Previous page](https://boards.straightdope.com/t/card-probability-aakk-out-of-a-deck/281241.md?page=1)