5 cards can be drawn from a single deck of 52 cards
An instructor has an exam of 5 questions and a question bank of 50 questions. Are there $50\choose 5$ or $(50)_5$ possible exams?
I am constructing a thought experiment about a spinning object that is floating in intergalactic space.  I assume that this object is about the size of a planet so that it will have enough gravity so that a Foucault pendulum will work, although I'm not sure that this is necessary for the thought experiment.    I can easily determine that this object is spinning if I stand on the object and observe the galaxies around me rise and set.  Similarly, I can determine the axis of rotation.    For simplicity, I go to one of the poles of my object, and I set up my Foucault pendulum.  What will I see?  And why will I see it?  I assume that in intergalactic space, the gravity is very small (galaxies are very far away, and the mass of my object is very small compared to the mass of a galaxy) so that there will be little coupling between the gravitational field of my object and the gravitational field of the galaxies around me. I am looking for an option to require a passcode to power off my iPhone. That way, if the phone is lost, the person who finds it cannot simply turn it off, rendering Find My iPhone useless. Is there a way to accomplish this? I'm currently developing a fake filesystem for a browsergame. I recently implemented ".." and "." folders so every folder has a reference to its parent. Then I checked in my terminal if "/" also has these folders.  Actually I was very surprised that it has a directory ".." which obviously is a reference to itself.  Is the reason for this consistency or is there a better explanation?  Edit: I'm basically looking for the document where this is documented. How do I design a 2A or more power supply for my consumer USB devices? I understand that many of my consumer devices charged by USB ports can charge at higher rates than 0.5A.  However, in testing, I've found they don't consume more than this. Test Setup  I have a power supply that outputs between 0 and 30 volts, and 0 to 20 amps. I set the voltage to 5 volts, then connected up a female USB to the wires correctly. When I plug in a Samsung Galaxy S4 Mini, it pulls around 0.44 amps. It is the same with a Samsung Galaxy Tab Pro. However, when I connect an iPad Air with an official lightning cable, it only pulls around 0.11 amps. Also, I tried connecting a ZGPAX S28 smartwatch and it was still about 0.44-0.45 amps.  The power supply is more than capable of outputting the maximum 2.1 amps, so why doesn't it to at least the tablets? What do I need to do in my test setup to convince the devices to consume their maximum charging current? World edit wood rotation Summation of natural number set with power of $m$ Who knows about the summation of this series: $$\sum\limits_{i=1}^{n}i^m $$  where $m$ is constant and $m\in \mathbb{N}$?  thanks How to know that your machine learning problem is hopeless? Imagine a standard machine-learning scenario:     You are confronted with a large multivariate dataset and you have a   pretty blurry understanding of it. What you need to do is to make   predictions about some variable based on what you have. As usual, you   clean the data, look at descriptive statistics, run some models,   cross-validate them etc., but after several attempts, going back and   forth and trying multiple models nothing seems to work and your   results are miserable. You can spend hours, days, or weeks on such a   problem...   The question is: when to stop? How do you know that your data actually is hopeless and all the fancy models wouldn't do you any more good than predicting the average outcome for all cases or some other trivial solution?  Of course, this is a forecastability issue, but as far as I know, it is hard to assess forecastability for multivariate data before trying something on it. Or am I wrong?   Disclaimer: this question was inspired by this one  that did not attract much attention. It would be nice to have detailed answer to such question for reference. Net work done on the body when we lift it and put it on the table is zero? $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral parsing XML file gets UnicodeEncodeError (ElementTree) / ValueError (lxml) I have an older Nvidia video card and my PC crashes when installing the driver for the video card in Ubuntu 16.04. When I get to the login screen but no further: after entering my password, the system went into a loop and returned always back to the login screen [with funny stripes present].   How do I fix this problem? Why is my StackOverflow with an indent and doesn't have reputation Well everything is in the title. Why is StackOverflow showing up with a indent and why don't I see my rep next to it like on the other websites. "Fake" 3d effect in Photoshop/Illustrator with raster images If "clearly evident" is redundant, what word or phrase suggests being indisputable but not readily apparent? A  asks whether the modifier "clearly" changes the meaning of "evident". I would have said, prior to examining a few dictionaries, that evident did not necessarily mean readily apparent, but to my surprise it does.  This brings me to ask what word or expression would mean something can be taken as a true fact, but not through an easily constructed (not obvious or readily apparent) rationale?   For example, if Sherlock Holmes says something is true while everyone else is still sitting on their hands, then it is evident to Holmes, but not to the rest of the world. So, from everyone else's point of view, it is not readily apparent, and (by definition) apparently it is not evident, clear, or clearly evident at all, based on the dictionary definitions. But (let's stipulate) it is true and deducible from the observable evidence. What would we call this?  Update  An update is highlighted above. I can see from some of the answers and comments that I may have gone off my mark with the phrase "not through an easy-to-follow rationale”, and I have modified the question to correct this. I understand that there can be rationales, arguments, or proofs that, once explained, may or may not be easy to follow. What I intend is that the rationale to support the indisputable conclusion is not (initially) easy to recognize or construct (not readily apparent) in the first place. I apologize for the confusion. (The original can be seen in the change history.)  Update 2  Shortly after offering a bounty to this request, I recalled a single word that I now believe is a very good match to the parameters specified in this inquiry as it is stated above. That word has not yet been suggested (or approached) by any answer or comment (active or deleted) at the time of this edit. This request is changed to a single word request. (However, if you feel a single word fits well but not without some additional supporting words, please offer your thoughts in an answer.) While my curiosity for the term has already been met, the request and bounty remain as an open challenge. I will post my own answer once the bounty has expired and been awarded. Interpreting Granger causality test's results I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online.  I also came across a very helpful tool, the , that allows you to enter your time series and calculate the Granger Stats.  Below, is the output from the sample data included on the site. I have also taken a crack at interpreting the results.   My Questions:     Is my interpretation directionally correct?   What key insights have I overlooked?   Also what is the meaning and interpretation of the CCF charts?  (I'm assuming CCF is cross correlation.)     Here are the results and plots that I have interpreted:  Summary of computational transaction Raw Input   view raw input (R code) Raw Output  view raw output of R engine Computing time  2 seconds R Server    'Herman Ole Andreas Wold' @ wold.wessa.net  Granger Causality Test: Y = f(X) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  17.9144959720894    2.94360540545316e-05  Granger Causality Test: X = f(Y) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  0.0929541667364279  0.760632773377753       My interpretation:    Test was based upon 357 data points and was performed with a lag value of 1 The p-value of 0.0000294 means I can reject the null hypothesis that x does not cause y for the Y = f(x). The p-value of .76 allows me to accept the null for X = f(Y) The fact that first hypothesis was rejected and second accepted is a good thing  I'm a little rusty on my F-test so I don't really have anything to say on this for now. I'm also not sure how to interpret the CCF graph.   I really appreciate it if any of you who are well versed with Granger-causality could let me know if I'm interpeting this correctly and also fill in some of the blanks.   Thanks for your help. Creating or adding geometry colunm fails even with postgis enabled Every time I open a folder from the desktop, a prompt is shown that the said folder is opened. How do I stop that? Can't change mouse influence in proportional editing mode I press O and I see it change to Proportional Editing mode, but when I press G and mouse wheel down/up, or arrow keys down/up, it doesn't change the influence area.    And I am, I press G and then I tried to scroll to change influence, but it's not working.    Done this aswell and it's not working Normally, LaTeX will only create references for the BibTeX entries cited in the text. Is there a way of extracting these entries into a different .bib file automatically? For example if I have a .bib file with two entries, and only one is cited in a particular text, I need a way of creating a new .bib file with just that reference. How are dual-role films shot?