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#1 2014-10-22 02:28:24

Hercules1946
Guest

Permutations

Hello
I am trying to establish how many permutations meet a particular criteria. There are six asset groups with a possible 18 weighting values. These are the numbers from 0.05 to 0.90 in steps of  0.05. So I need to establish how many different permutations of these numbers can be allocated to the 6 groups.
Repeated use of the same number is allowed, and the same 6 numbers in a different order is allowed so:
0.05, 0.05, 0.05, 0.05, 0.05, 0.75 is valid, and so is 0.75, 0.05, 0.05, 0.05, 0.05, 0.05 so both would count.

So I think the formula here is  18^6 = 34012224 permutations, but then there is a condition to apply, and Im not sure how to do this. The 18 values are fractions of 1 and the full total of permutations must be filtered such that those with 6 fractions that add up to one are the only valid permutations (like the two examples above).
I coud be wrong about the formula, because (eg) mathematically you may need to repeat each instance of 0.05 in all six positions, but for this exercise, those repeats would not be valid as
the weight value for each asset would still be 0.05. Hope that makes sense!

Can anyone help with this?

Thanks in Advance

smile

#2 2014-10-22 02:45:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

I am trying to establish how many permutations meet a particular criteria. There are six asset groups with a possible 18 weighting values. These are the numbers from 0.05 to 0.90 in steps of  0.05. So I need to establish how many different permutations of these numbers can be allocated to the 6 groups.

I am not following the group idea.  Are you are thinking about this as a big line of values

.5  .1 .6 .05 .9 .25 .35 .7 .9 .1 .15 .85 .8 .75 .15 .2 .5 .6

like that.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2014-10-22 07:50:34

Hercules1946
Member
Registered: 2014-10-22
Posts: 5

Re: Permutations

Hello bobbym
Im sorry if I didn't make things clear.
1. The permutations will be selected from 18 numbers ranging from 0.05 to 0.90 at intervals of 0.05 (so... 0.05, 0.10, 0.15 .... etc).
2.  These numbers represent weighting factors that can be applied to six groups of assets, and we need to establish how many different sets of six that we can pull from the 18.
3. Its OK for the same weighting factor to be used on multiple asset groups, as long as the six factors total 1 (one) which is a requirement for all valid sets.
4. Examples:
    Asset 1     Asset 2    Asset 3    Asset 4     Asset 5    Asset 6
     0.05          0.05        0.05        0.05         0.05        0.75       OK
     0.05          0.75        0.05        0.05         0.05        0.05       OK
     0.10          0.20        0.05        0.10         0.40        0.15       OK
     0.10          0.20        0.30        0.40         0.50        0.60       Not OK because sum is > 1 (2.10).

5. So the question is: How many sets of 6 can be obtained from the 18 numbers, where the sum of the 6 vaues is equal to 1 ?

Proviso: Although one of the 18 factors can be used up to 5 times in a set of 6, it would not be valid to make another permutation by exchanging one of these for another of the same value as this would have no affect on any weight calculation.  In other words 0.05 x Asset 5 will be the same no matter which instance of 0.05 is used.
In contrast, the change betwwen the first two examples above is a different permutation because 0.75 x Asset 6 will be different from 0.75 x Asset 2.

Hope that answers your questions

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#4 2014-10-22 08:32:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

Hi;

Okay bear with me. So you allow that

    0.05          0.05        0.05        0.05         0.05        0.75       OK
    0.05          0.75        0.05        0.05         0.05        0.05

are to be counted as 2 different ways?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2014-10-23 01:13:50

Hercules1946
Member
Registered: 2014-10-22
Posts: 5

Re: Permutations

Hello - and thanks for your help.
Yes, they are two valid permutations. The user is trying to size how many possible sets of permutations he needs to allow for, and any permutation that results in a different total valuation of the assets is to be counted.
In the example, the criteria is true because Asset No:6 x 0.75 (set 1) will be different from Asset No:2 x 0.75 (set 2), giving two different totals.

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#6 2014-10-23 02:44:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

Hi;

I am getting 11628 ways.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2014-10-23 05:16:41

Hercules1946
Member
Registered: 2014-10-22
Posts: 5

Re: Permutations

Thats great!  Thank you very much!
Can you explain how you did it so I can replicate, and get a listing of the groups, as Is provided in the permutations calculator ?

Last edited by Hercules1946 (2014-10-23 05:17:18)

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#8 2014-10-23 05:25:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

I used Mathematica to do the counting for one way and used a generating function for another way.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#9 2014-10-23 07:30:09

Hercules1946
Member
Registered: 2014-10-22
Posts: 5

Re: Permutations

I tried with multiple use of the web sites' permutation calculator, and I got 11778 ways, so I must have made a mistake somewhere. I will have to recheck.

Thanks again for your help.

smile

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#10 2014-10-23 07:46:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

Let me check mine.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#11 2014-10-23 07:52:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

Let me check mine. I am getting 11628 again.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#12 2014-10-23 09:53:30

Hercules1946
Member
Registered: 2014-10-22
Posts: 5

Re: Permutations

Hi
Just to let you know, Ive rechecked my figures, and when recalculating the extra permutations for the sort order of the sets, I'd allocated the wrong pattern to a couple of them and that overstated the permutations.
Ive now got the listing to support 11628 permutations.

Thanks very much for your help.

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#13 2014-10-23 19:13:11

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Permutations

You are welcome.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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