# Please Explain (mathematics question) **URL:** \ **Category:** Factual Questions\ **Created:** [March 7, 2011, 5:19pm UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797 "2011-03-07T17:19:17Z")\ **Posts on this page:** 10\ **Page:** 2
**Author:** ![J\_Cubed](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@J\_Cubed](https://boards.straightdope.com/u/J_Cubed)\ **Post date:** [March 8, 2011, 3:22am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/21 "2011-03-08T03:22:26Z")
> [@RadicalPi](#): > > I don’t know if anyone’s mentioned it, but ! represents the factorial function. 0! time, in 6.5238!, for 3.878! minutes. ---
**Author:** ![SeldomSeen](https://avatars.discourse-cdn.com/v4/letter/s/7ba0ec/32.png) [@SeldomSeen](https://boards.straightdope.com/u/SeldomSeen)\ **Post date:** [March 8, 2011, 3:35am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/22 "2011-03-08T03:35:55Z")
Thanks to all who responded, explaing a difficult (for me) problem in layman’s terms. I believe I understand it better now. SS ---
**Author:** ![Spectre\_of\_Pithecanthropus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spectre_of_pithecanthropus/32/12343_2.png) [@Spectre\_of\_Pithecanthropus](https://boards.straightdope.com/u/Spectre_of_Pithecanthropus)\ **Post date:** [March 8, 2011, 6:54am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/23 "2011-03-08T06:54:28Z")
> [@Malacandra](#): > > _[sup]n[/sup]C[sub]r[/sub]_. > > Written as [noparse]_[sup]n[/sup]C[sub]r[/sub]_[/noparse]. Thanks for replying. The symbol I’ve seen is different, but it was in a very old textbook so I wouldn’t be surprised if it’s obsolescent. This was a tall set of parentheses with containing _n_ and _r_, one positioned over the other. Or is that something else? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [March 8, 2011, 7:04am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/24 "2011-03-08T07:04:20Z")
No, writing _n_ over _r_ in vector parentheses means the same thing, but defeats my coding skills! ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 8, 2011, 7:33am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/25 "2011-03-08T07:33:06Z")
Quoth **Wendell** : > [@](#): > > You seem to think that it would be necessary to produce about (10^68) different orderings to expect to see even one case where two of those orderings match. That’s not true. It’s only necessary to produce about (10^34) different ordering to expect to see about one case where two of those orderings match. But that’s not what **brocks** said. He didn’t say that if all those people shuffled for all that time that they’d never match _each other_; what he said was that they’d never match _that one specific shuffling you did_. ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [March 8, 2011, 10:07am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/26 "2011-03-08T10:07:26Z")
Now that I reread what brocks wrote, I’m not clear what he meant. If he means that one starts with a given ordering and waits until that ordering is repeated, then his calculations are correct that about random (10^68) orderings have to be produced. If he means that one starts producing orderings and waits until there is some repetition, then my calculations that one only needs to produce (10^34) random orderings to see the first repetition are correct. ---
**Author:** ![DHMO](https://avatars.discourse-cdn.com/v4/letter/d/ecc23a/32.png) [@DHMO](https://boards.straightdope.com/u/DHMO)\ **Post date:** [March 8, 2011, 10:34am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/27 "2011-03-08T10:34:50Z")
> [@Wendell\_Wagner](#): > > Now that I reread what brocks wrote, I’m not clear what he meant. If he means that one starts with a given ordering and waits until that ordering is repeated, then his calculations are correct that about random (10^68) orderings have to be produced. If he means that one starts producing orderings and waits until there is some repetition, then my calculations that one only needs to produce (10^34) random orderings to see the first repetition are correct. I think it is very clear what brocks meant: > [@brocks](#): > > If you shuffle a deck thoroughly, then you have produced something that the world has never seen before, and if left only to chance, will never see again. > … the chance that one of them would have produced \*\*\*the same order of cards you did \*\*\*would be about one in a trillion trillion. [emphasis mine —DHMO] ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [March 8, 2011, 10:58am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/28 "2011-03-08T10:58:41Z")
Incidentally, even if you assume that’s what he meant, his arithmetic still isn’t quite correct. As I showed in my calculations, he’s talking about (10^53) different orderings being produced. He claims that there’s only one chance in a trillion trillion that this will match a given ordering. But there are only about (10^68) different orderings, so that’s one in a thousand trillion, not one in a trillion trillion. And I still don’t find it clear what he meant, but this is pointless to argue about. ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [March 8, 2011, 11:39am UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/29 "2011-03-08T11:39:34Z")
> [@J\_Cubed](#): > > It’s six of one thing, 3! of the other. Just thought I should say this is a pretty clever joke but somehow seems to have caused the thread to turn to crap. ---
**Author:** ![brocks](https://avatars.discourse-cdn.com/v4/letter/b/7feea3/32.png) [@brocks](https://boards.straightdope.com/u/brocks)\ **Post date:** [March 8, 2011, 2:11pm UTC](https://boards.straightdope.com/t/please-explain-mathematics-question/573797/30 "2011-03-08T14:11:10Z")
> [@Wendell\_Wagner](#): > > Incidentally, even if you assume that’s what he meant, his arithmetic still isn’t quite correct. As I showed in my calculations, he’s talking about (10^53) different orderings being produced. He claims that there’s only one chance in a trillion trillion that this will match a given ordering. But there are only about (10^68) different orderings, so that’s one in a thousand trillion, not one in a trillion trillion. > And I still don’t find it clear what he meant, but this is pointless to argue about. You’re right, I somehow managed to add 54 to 24 and get 68. But I’m danged if I can see how you find it unclear that I’m specifying a particular deck to match. [Previous page](https://boards.straightdope.com/t/please-explain-mathematics-question/573797.md?page=1)