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#1 2012-11-08 10:25:20

Blitz
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combination number...

Hi,

I`ve carefully read this site's in depth explanation regarding combinations and permutations and I`ve learned a lot.

However... I have two questions:

1. I am still searching a formula that can give me the RANKING POSITION of a combination. I`ll give an example:

lottery numbers : 5 numbers are chosen from 50 numbers. this gives 2118760 possible combinations, from 1-2-3-4-5 to 46-47-48-49-50.
Now I need a formula that gives me the ranking position (from 1 to 2118760), when I enter the 5 chosen numbers in the formula. For example, combination 1-2-3-4-6 should return ranking position #2, combination 1-2-3-4-7 should return 3, and so on.

What is the formula for this?

2. I have noticed that the Combinations and Permutations Calculator on this site calculates the result at any keystroke. This makes me believe it uses a non-recursive factorial function. So far, I haven't found any non-recursive factorial math function (to use in visual basic for example). I have used a recursive factorial function so far, but when the number of possible combinations gets too high, I get -an expected- stack overflow. What function does this website use?

#2 2012-11-08 10:56:34

bobbym
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Re: combination number...

Hi Blitz;

A couple of questions, usually formulas are given for permutations.

Do you want {1,2,3,4,5} to be different than {5,4,3,2,1}? Then we are dealing with a permutation.

There is an algorithm to do this:

Let's say you want the position and I have picked small numbers to better illustrate, {4,7,9,10,11}



For {1,2,3,4,7} we get:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-11-10 09:32:43

Blitz
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Re: combination number...

bobbym wrote:

A couple of questions, usually formulas are given for permutations.

Do you want {1,2,3,4,5} to be different than {5,4,3,2,1}?]

No, so I think we're talking about combinations here.

Can you explain your example please, because I don't see how {4,7,9,10,11} results in your formula

and how do you write

as a plain formula?

#4 2012-11-10 11:47:27

bobbym
Administrator

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Re: combination number...

Hi Blitz;

Like with the permutations there is no formula just an algorithm or method.

For the second question:



so


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2012-11-12 11:01:04

Blitz
Novice

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Re: combination number...

Blitz wrote:

So here's the same question : Can you explain your example please, because I don't see how {4,7,9,10,11} results in your algorithm. I don't see the link between 4,7,9,10,11 and the numbers in your algorithm:

Thx for clarifying the second question.

#6 2012-11-12 11:26:33

bobbym
Administrator

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Re: combination number...

Hi;

Supposing we have {4,7,9,10,11} out of the numbers 1 to 20.
The first combination is 1,2,3,4,5 and the last is 16,17,18,19,20.

Start with the first number which is 4.

There are 19 C 4 combinations of the type 1,xxxx
There are 18 C 4 combinations of the type 2,xxxx
There are 17 C 4 combinations of the type 3,xxxx

so we have



There are 15 C 3 combinations of the type 4,5 xxx
There are 14 C 3 combinations of the type 4,6 xxx

so we have



There are 12 C 2 combinations of the type 4,7,8 xx

so we have



add 1 for the next one.



Want to do another?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2012-11-13 11:05:54

Blitz
Novice

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Re: combination number...

I get it now. Thanks for explaining!

#8 2012-11-13 11:11:45

bobbym
Administrator

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Re: combination number...

Hi Blitz;

You are welcome. You understood that fast, very good.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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