The question is $n$ students are standing in a circle.  Find the number of ways in which $k$ students can be selected such that no two of them are together. I know one method to do this by comparing it with a question like &quot;find number of triangles that can be formed inside an $n$-sided polygon such that no side of triangle is common to the $n$-sided polygon&quot; but that'll be valid only when $k=3$. I want to know general method to solve such questions and also the principle behind that method. Any help appreciated 😃
In how many ways can we choose k items from n distinct items put in a circle.   Then further extension of the question, if I want to find out the number of ways to choose k items from n distinct items in a circle such that no 2 are together.  Thanks
Prevent specific sites from being overrepresented in the hot questions list Some sites appear far more often in the hot questions list than other sites. I don't have any hard data on that, as that kind of data is just not publicly available, but I'm pretty sure my subjective impression on that is reasonably accurate.  Those sites don't appear more often because they are inherently more interesting, but because they have certain voting and answering patterns that favor them in the hot questions algorithm. I would argue that the goal of the hot questions list is to present questions from a large variety of SE sites to the whole network, and to show possibly interesting questions to users that would not have found them otherwise.   To achieve this goal, the spots in the hot questions list should be distributed among all SE sites. The algorithm should try to get a good sampling of all sites, and it should try to normalize the results for varying voting behaviour. At the moment, sites that intrinsically get more votes and more answers per question seem favored in the algorithm.  So I think one part of the algorithm should try to identify questions that get an unusally high amount of votes and views for that site, and give the smaller sites a chance this way.  I'm not sure on how exactly this weighting should be done, as a complete normalization would likely not work across the huge difference in scale for all the SE sites.  As a specific example that the current algorithm is broken I'll present . I don't think any site should occupy a third of the whole list.   Here's another instance where one site is overrepresented at the top of the list: What is the command to truncate a SQL Server log file? I need to empty an LDF file before sending to a colleague.  How do I force SQL Server to truncate the log? How is the popularity of "recent tags" calculated? How are these calculated? I see them going up and down all the time, and there are obviously way more than 48 questions about C# so how are these calculated? Indian passport threading coming off My Indian passport threading is coming off i.e. the cover of the passport is coming off, there are only 2 threads remaining.   Will it be a problem at the airport when going abroad ? Also anyone who has experience of getting a replacement passport fairly quick ? Because I need to get a passport in like 15 days. Converting a DC motor to a generator Can ANY DC motor become a generator if torque is applied to the shaft? example:   And by any, I mean the really cheap ones too.  Or is there a specific type of motor (of which I do not know the name) that can work in both directions (battery to power the shaft OR torque-on-shaft to create a voltage difference between the terminals). Some GUI apps use OS X location services, but I want to retrieve a Mac's physical location from the . This could be useful for running scripts, switching settings etc. The mechanism should be , not a Geo IP service (data too low-res, needs online connection).  Minimum requirement is output of longitude and latitude. Nice would be a number indicating the precision. Super nice: a geocoder that provides location names. Posting a Solution of a problem that You faced to Help Newbies About an Hour ago, I faced a problem and tried different ways to solve it.  At last I was going to post my Question on Stack Overflow, but the last trick which came in my mind worked, and the problem got resolved.    Now, if I want to post that problem on Stack Overflow with the solution which worked for me, for the purpose to help other newbies to get their answer if they face the same problem, what is the proper way of posting such solution to a problem? Note: this post is different to , which just cites part from somewhere else, without any further analysis and thinking. Furthermore, none of the answers to that post answers my question - the situations where &quot;will (going to) be doing&quot; is more appropriate.   I will be participating in IELTS test next Tuesday afternoon.  In an online class, the teacher says the following at the beginning of the lesson.  I will be using NotePod (pointed out by red rectangle) to write relevant points we talk about today.   I guess &quot;will be using&quot; is more appropriate than &quot;will use&quot; there, right?  A  explains  This &quot;tense&quot; is used for reporting a scheduled activity with special focus on its timing— as if one is standing in the future and experiencing the flow of the time. The focus is on the temporary, ongoing, or repetitive nature of the activity.   I understand the grammar rules of those verb tenses and the difference between this group  I am going to drive home tomorrow.   I am going to be driving home tomorrow.  The former is just convey my activity in the near future while the latter probably makes an implication that &quot;don't disturb me as I am driving in that time&quot; However, in the following situations, I don't see the difference between 2 verb tenses.  Welcome back to this class. Today's lesson is for the IELTS students who are going to be taking the IELTS test. it's for everybody to be honest with you. this lesson is useful for anybody who needs to do some writing.   who are going to take the IELTS test ... Review Queues and Ignored Tags Steps to Recreate:   Have enough rep to use some of the review queues. Ignore a popular tag. Go to your profile-> prefs-> check 'hide ignored tags'. Open a review queue.   You will get questions from your ignored tag(s) in the review queue.  Personally, I ignored a tag on Movies.SE (and Scifi.SE) for a film that is out elsewhere in the world, but not locally.  It's a simple way to avoid being exposed to spoilers.  I then load up the First Posts review queue on Movies.SE, and I get an answer to a question about the end of the film.  Can the review queues be altered to skip posts on your ignored tags when you have the 'hide ignored tags' option enabled? I Cancelled Microsoft 10 Reservation and uninstalled KB3035583 but Window 10 is still trying to install I cancelled the Microsoft Windows 10 Reservation and uninstalled KB3035583, but Windows 10 is still trying to install.   After I uninstalled KB3035583 and restarted my laptop as instructed, I could not find KB3035583 to hide it.   Now Windows 10 is sitting in my Windows Update saying that it will install when I restart my computer. I want to do research but I'm too old for a PHD I really love research. I started a research project in graduate school for my M.A. in English. My research topic is a very viable and interesting topic for a dissertation. I'll be 60 on my next birthday and I know that many Ph.D programs are traditionally geared toward younger students.I was wondering are there any programs that I can continue this research in without facing the issues of ageism in academia? How to use siunitx with non numerical values? I understand that something like \SI{5}{\meter\per\second} defines a certain space between the number (5) and units (m/s). What should I use if instead of a numerical quantity I want a variable: R m/s? \SI{R}{\meter\per\second} fails because it expect a number in first parameter, and R \si{\meter\per\second} or $R$ \si{\meter\per\second} show different space.  Which is the correct use?  \documentclass{standalone} \usepackage{siunitx} \sisetup{per-mode=symbol} \begin{document} \begin{tabular}{r} \SI{5}{\meter\per\second}\\ $R$ \si{\meter\per\second}\\ R \si{\meter\per\second}\\ \end{tabular} \end{document} Convert audio stream to WAV byte array in Java without temp file Hosting multiple distinct folders for distinct domains Create hexagonal mesh on 3D Parametric Plot and 3D spheres? Content Type field on NewForm.aspx I have a custom list and I am using content types to add items to the list. I am using OOTB forms for new and edit items. One field that I see on the EditForm.aspx is the one that I hope I get on the NewForm.aspx also and it is the Content Type field. It is shown in the following screenshot. Do you know how to add that field on the NewForm.aspx page also?    Thanks. Check out the screenshot below, I want to extend my C partition (where Windows is installed) into the unallocated free space shown. This space was cleared up by shrinking the D partition. I can extend the D partition if I want to, but not the C.  Why not? How do I evolve Kadabra to its final form without trading it? TL:DR: Is it ever a good idea to train an ML model on all the data available before shipping it to production? Put another way, is it ever ok to train on all data available and not check if the model overfits, or get a final read of the expected performance of the model?    Say I have a family of models parametrized by $\alpha$. I can do a search (e.g. a grid search) on $\alpha$ by, for example, running k-fold cross-validation for each candidate.   The point of using cross-validation for choosing $\alpha$ is that I can check if a learned model $\beta_i$ for that particular $\alpha_i$ had e.g. overfit, by testing it on the "unseen data" in each CV iteration (a validation set). After iterating through all $\alpha_i$'s, I could then choose a model $\beta_{\alpha^*}$ learned for the parameters $\alpha^*$ that seemed to do best on the grid search, e.g. on average across all folds.  Now, say that after model selection I would like to use all the the data that I have available in an attempt to ship the best possible model in production.  For this, I could use the parameters $\alpha^*$ that I chose via grid search with cross-validation, and then, after training the model on the full ($F$) dataset, I would a get a single new learned model $\beta^{F}_{\alpha^*}$   The problem is that, if I use my entire dataset for training,  I can't reliably check if this new learned model $\beta^{F}_{\alpha^*}$ overfits or how it may perform on unseen data. So is this at all good practice? What is a good way to think about this problem? These are my current disk partitions. /yedek is for some personal backup files. As you can see there is only Ubuntu on my PC. I will install Windows, too. Because of this I want to shrink /dev/sda3 . It currently 546GB and I want to split it: 300GB for / and 246GB for Windows (NTFS) is OK for me.  I'm using GParted for the first time. How can I shrink /?  I don't want to lose any datas from Ubuntu.