
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 12345 to 4647484950. 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 12346 should return ranking position #2, combination 12347 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 nonrecursive factorial function. So far, I haven't found any nonrecursive 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?
 bobbym
 Administrator
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.
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?
 bobbym
 Administrator
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.
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.
 bobbym
 Administrator
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.
Re: combination number...
I get it now. Thanks for explaining!
 bobbym
 Administrator
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.
