Talk:Combination

message: : {n \choose k} = \frac{n!}{k! \cdot (n-k)!}. 
The most obvious method of obtaining the numerical value given above is not the 
most efficient method. This is most inefficient if the value of n is very large.
A more efficient algorithmn for the numerical value is 
: {n \choose k} = \frac { ( n - 0 ) }{ (r - 0) } \times \frac { ( n - 1 ) }{ (r - 1) } \times \frac { ( n - 2 ) }{ (r - 2) } \times \frac { ( n - 3 ) }{ (r - 3) } \times \cdots \times \frac { ( n - (r - 1) ) }{ (r - (r - 1)) }
Example:
: {70 \choose 4} = \frac { 70 }{ 4 } \times \frac { 69 }{ 3 } \times \frac { 68 }{ 2 } \times \frac { 67 }{ 1 } = 916895
:That is true.  But one should add that after putting it in the form
:: {70 \choose 4} = \frac { 70 }{ 4 } \times \frac { 69 }{ 3 } \times \frac { 68 }{ 2 } \times \frac { 67 }{ 1 }
:one should CANCEL BEFORE MULTIPLYING. Michael Hardy 23:53, 30 August 2005 (UTC)
thread_title: Efficient calculation

message: Wouldn't it be more consistent to have the term representing combinations in the same style as the term representing permutations? Combinations is (n k) and Permutations is P(n, k). I suggest C(n, k) would be better.   David Ball 01:58, 28 December 2005 (UTC)
thread_title:  Consistency in style 

message: This "Merge" talk section (about merging the substance of what was then the article "Permutations and combinations") incorporated article text, including what was presumably a heading "Combination with repetition" from that article. (For the record, probably the level (depth) of the heading was changed to better fit the environment of this talk page.)   For the record, that other page got renamed from "Permutations and combinations" to "Twelvefold way".   I'm acting in the hope that additional (parenthesized) headings, and an (additional) level change, will help make it more intuitive than it was as i found it.--Jerzy•t 02:05, 26 July 2014 (UTC)
thread_title:  (Meta-talk) 

message: (Note: except for retrofitted parenthesized section headings, everything in this sub-section is part of a single talk contribution.)
==== (Initial (& original) content) ====
I'm doing the merge now. The following section was in the article but seems to contradict this article:
==== (Heading, and prose content, imported from WP "Permutations and combinations" article (a.k.a. "Twelvefold way") ====
===== Combination with repetition =====
When the order does not matter and an object can be chosen more than once, then the number of combinations is
:{{(n + r - 1)!} \over {r!(n - 1)!}} = {{n + r - 1} \choose {r}} = {{n + r - 1} \choose {n - 1}}
where n is the number of objects from which you can choose and r is the number to be chosen.  This can be visualised in the following way: Imagine a string of n symbols, from which we choose r examples. e.g. pick eight symbols from the list {a, b, c, d, e}.  We can rewrite this using the symbols 1 and /, meaning 'choose one' and 'next symbol' respectively.  Therefore a choice of, say, {a, a, b, c, c, c, e, e} could be represented, starting at 'a', as {1,1,/,1,/,1,1,1,/,/,1,1}. ("Choose an 'a'; choose another 'a'; move on to the next symbol, 'b'; choose a 'b';" etc.) This is an equivalent to choosing n − 1 positions for the / symbol in a string of length (n − 1) + r, where n = 5 and r = 8 in this example. Thus this problem is equivalent to choosing n - 1 positions from amongst n + r − 1, without repetition, and hence falls under a previously described case.
For example, if you have ten types of donuts to choose from and you want three donuts there are 
:{{(10 + 3 - 1)!} \over {3!(10 - 1)!}} = {220} 
ways to choose (see also multiset).
==== (Further (& original) comment, by includer, on the embedded section; also includer's sig) ==== 
Is this right? If so, please incorporate into the article.Tocharianne 19:05, 31 December 2006 (UTC)
thread_title:  (Contrib that embedded an "imported" heading into this talk page) 

message: Is this right? If so, please incorporate into the article.Tocharianne 19:05, 31 December 2006 (UTC)
thread_title:  (Further (& original) comment, by includer, on the embedded section; also includer's sig) 

message: : Yes it is right. It is proved twice in multiset. No need to repeat it here.--Bo Jacoby 21:46, 31 December 2006 (UTC)
replies: text: Hi, I've added an alternative explanation.--Bizso (talk) 22:06, 15 April 2009 (UTC)
thread_title:  (Contribs responding to includer) 

message: If K is "any number greater than 1 and smaller or equal to N"? What kind of combination without repetitions is it and what's the shorthand equation? How can one calculate the amount of of combinations possible if a P amount of the elements at hand can be exchanged with an F amount of alternatives yet none to L or all of P can coexist with none to L or Q or all of FUndead Herle King (talk) 19:35, 5 April 2008 (UTC)
thread_title: But what if?

message: Shouldn't this article at least make a passing reference to pascal's triangle, and mention some algorithms for calculating combinations?  Antares5245 (talk) 08:50, 25 July 2009 (UTC)
thread_title: Pascal's Triangle, Algorithms

message: There have now been two successive unmotivated undoes by 76.251.40.133 (talk) of the same edit, with a few days' interval. I've reverted a second time, but would not like to go into edit warring. Given this user's (or IP's) track record, I guess it is just vandalism, and measures should be taken if it recurs again. Of course if there is any motivation for the undoes, this is the place to explain. Marc van Leeuwen (talk) 11:20, 21 February 2010 (UTC)
thread_title:  Repeated undoes 

message: I have done an extensive research on Permutation and combination. I have also found a convenient method of numbering permutation. This convenient method of counting combination is presented in some of the word document which is attached to my sight.
https://sites.google.com/site/junctionslpresentation/home 
The eminent method of counting combination is represented as C-Junction or C-Junction Number(CJN) and also mentioned as Combination order number(CON).
But the CJN and CON are different terms which is mentioned  in this site
in my word document.— Preceding unsigned comment added by 14.97.31.204 (talk) 14:04, 23 May 2012 (UTC)
replies: text: The word documents are pasted at the bottom of this page.https://sites.google.com/site/junctionslpresentation/proof-for-advance-permutation  — Preceding unsigned comment added by 14.97.31.204 (talk) 14:27, 23 May 2012 (UTC)
thread_title:  An eminent way to count the combination of objects.  

message: I consulted Help:Displaying_a_formula as well as Google searched, but I couldn't figure out how to either ensure the package is being included, and therefore determine if the issue is on my end, or to include the package manually. Are any other MathJax users having issues? Curtis (talk) 21:15, 13 March 2014 (UTC)
thread_title:  MathJax not rendering cancellations in Firefox 

message: The math notation that (in the frequent case where nothing about the context makes unsuitable either n or r as names for the two arguments, variables, or parameters) is read aloud as either
* "n C r",
* "combinations of n things taken r at a time", or
* "n chose r".
Its symbol can be wiki-coded as either nCr or nCr. (Our article prefers n and k, to the point of not even mentioning r, by the way.)    IMO, exhibiting only with what looks to me like the (still IMO fairly exoteric) TeX representations (tho they work too well to favor the wiki-markup versions) is likely to be intimidating to non-professionals; we should discuss the combinations notations over a range (typewriter thru Tex or even more professional) of typographic standpoints somewhere, and link there from the acc'g article (if that place is not the accompanying article). --Jerzy•t 08:05, 26 July 2014 (UTC)
thread_title:  n-Choose-r 

message: It is common place to accuse people in rollback without talk, when you (initiate) rollbacks without talk. That is one reason why it is difficult to talk to people who expose such behaviour. Another is that they refute meaningful and easily verifiable information on the grounds that they are final instance of expertise and if something is not familiar to them, it is not standard, as "one gentleman classified my edit" . Why do they think that if that something they have never heard of is non-standard? At first, the notion of variations makes sense to complement permutations and combinations. Secondly, there are thousands of references in the google so that it is difficult to choose one as a reference. They are well known in Russian schools and authors of ru:Размещения had a difficult time to find English counterpart before I had created the article on  variations. Wait, at first, nobody has right to label something non-standard and unsourced while there is a corresponding article in the Wikipedia. It is a vandalism to remove links to the valid Wikipedia articles under pretext that the link is unsourced. How can a reference to the source be unsourced? You cannot call an article in Wikipedia not a source. There is no excuse for User:Wcherowi behaviour. --Javalenok (talk) 09:04, 19 August 2014 (UTC)
replies: text: It is nonstandard in English mathematical literature.  Perhaps there is another term, but k-permutations seems adequate.  — Arthur Rubin  (talk) 17:05, 24 August 2014 (UTC)
thread_title:  Militant ignorance against [[variations (Combinatorics) | vairations]] 

message: I have now twice reverted 's insertion of generalized binomial coefficients into the section on multset coefficients. My edit summary indicated that this notation had not been defined in this article (or linked to for that matter) and with the conventions in use in this article this would be confusing. Given the elementary nature of the article, I think this notation is out of place. At the very least, its use in these formulae would require citations to reliable secondary sources. It may be true that their use gives a more elegant formulation, but elegance is only a desirable trait for a sophisticated mathematical audience and is not particularly useful in an encyclopedia.--Bill Cherowitzo  (talk) 20:00, 20 April 2017 (UTC)
replies: text: This "generalized" notion is explained in binomial coefficient article linked from here. It's not a problem to add the definition here as well (is that your request?). Notice that you not only deleted generalized binomial coefficients but also the generating functions for \left(\!\!\binom{n}{k}\!\!\right) -- what's wrong with them? Maxal (talk) 20:05, 20 April 2017 (UTC)

text: I do not see a problem in using generalized binomial coefficients, when they are given in parallel with traditional ones. They are very natural in this context and allow derive the g.f. easily. I disagree that their use is not useful  in encyclopedia (by similar arguments you may easily suggest to remove half of the binomial coefficient article). Encyclopedia should be comprehensive at first place (and elegant when possible). Maxal (talk) 20:21, 20 April 2017 (UTC)
thread_title:  Use of generalized binomial coefficients in this article 

message: Is it accurate to use the word "sequence" in the first sentence considering order is supposedly not taken into account?
The second sentence discusses the number of such samples, so it is not really "In other words" from the first sentence; it is a (slightly) different issue.  — Preceding unsigned comment added by Aliotra (talk • contribs) 17:30, 3 February 2021 (UTC)
replies: text: You are correct on both counts.  Feel free to improve it :).  --JBL (talk) 17:51, 3 February 2021 (UTC)
thread_title:  Number of combinations with repetition 

message: Feel free to use this image.  I am working on a Wikiversity article that explains this in detail. --Guy vandegrift (talk) 18:53, 5 September 2021 (UTC)
thread_title:  Proposed image illustrates that items are unlabled. 

message: Is there the definition for negative k? Ans (talk) 21:07, 28 January 2024 (UTC)
replies: text: There is a very thinly referenced section here about allowing the lower index in a binomial coefficient to take on more general values than nonnegative integers, but really this does not ever seem to come up in other contexts. --JBL (talk) 22:16, 28 January 2024 (UTC)
replies: text: But the gamma and beta function in that section is undefined when y is negative Ans (talk) 11:37, 29 January 2024 (UTC)
thread_title:  negative k? 

message: The redirect NCr has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  Shhhnotsoloud (talk) 18:52, 6 February 2024 (UTC)
thread_title:  "[[:NCr]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]