|
|
 | | From: | Kenneth Brun Nielsen | | Subject: | Permutations | | Date: | Wed, 19 Jan 2005 23:40:18 +0100 |
|
|
 | Hi all,
I forgot my theory...
How many permutations are there among 17 numbers?
That is for the array [1,2...17] : [1], [1,2],[1,3]....[1,2,..,17].
How many?
/Kenneth
|
|
| | From: | Fred Curtis | | Subject: | Re: Permutations | | Date: | Thu, 20 Jan 2005 01:02:11 +0000 (UTC) |
|
|
| Kenneth Brun Nielsen wrote:
> I forgot my theory...
>
> How many permutations are there among 17 numbers?
>
> That is for the array [1,2...17] : [1], [1,2],[1,3]....[1,2,..,17].
>
> How many?
http://mathworld.wolfram.com/Permutation.html
|
|
| | From: | Fred Curtis | | Subject: | Re: Permutations | | Date: | Thu, 20 Jan 2005 01:29:50 +0000 (UTC) |
|
|
| Fred Curtis wrote:
> Kenneth Brun Nielsen wrote:
> > I forgot my theory...
> >
> > How many permutations are there among 17 numbers?
> >
> > That is for the array [1,2...17] : [1], [1,2],[1,3]....[1,2,..,17].
> >
> > How many?
>
> http://mathworld.wolfram.com/Permutation.html
Unless, of course, you're not actually counting permuations.
I assumed you were using a notation for cyclic decompositions
for permutations and wanted:
* the number of ordered arrangements of 17 objects, in which
case the answer is 17! = 17*16*...*2*1 -- 17 choices for
the first object in the list, 16 for the second object etc.
If you were using the cyclic decomposition notation, then
there are the same number of permutations (considered as
operators-on-arrangements) as permutations (considered as
arrangements)
but you might be trying to count:
* the number of unordered subsets of a set of 17 objects,
e.g. treating [1,2,3] as the same as [3,1,2] and [1,3,2] etc,
in which case the answer is 2^17 (each object can be either in
the subset or not), which includes the empty set [].
or
* the number of ordered subsets of a set of 17 objects,
e.g. treating [1,2,3] as different to [3,1,2] etc,
in which case the answer is floot(n! * e).
|
|
|
