A tennis club has 40 members. They host a tournament playing single   (one verses one) matches. Every member of the club plays one match   with another member of he club, so twenty matches are held. (a) In how   many ways can this be arranged?   I was a little confused by the wording of this question in regards to the teams being 'arranged' but I was wondering if it is as simple as the number of ways to choose 20 different match setups, i.e number of ways to choose two different people out of 40. So tried:  C(40,2) and wasn't sure if I needed to multiply by the number of people: so C(40, 2) * 40. I also thought this could be a circular arrangement problem but wasn't sure.. Am I on the right track or way off here?
Apparently, there are $\frac{(2n)!}{2^nn!}$ ways to break $2n$ people into partnerships. Why?   An explanation reads that there are $2n!$ ways to line people up. If we just pair adjacent people in the line up, we would have overcounted. So we must divide by $2^n n!$.  My question is why do we divide by $2^n n!$ specifically to adjust for overcounting?  Furthermore, this problem can apparently be solved by taking a skip factorial of odd values:  $(2n-1)(2n-3)(2n-5) ... (5)(3)(1)$  Why is that so? What does this skip factorial have to do with the problem?
Difference between $ and # in Linux environment Irrationals: A Group? I understand that the set of irrational numbers with multiplication does not form a group (clearly, $\sqrt{2}\sqrt{2}=2$, so the set is not closed). But is there a proof or a counter-example that the irrationals with addition form (or do not form) a group?  Thank you!  Edit: In particular, I am wondering if the set is closed with respect to addition. In every keyboard that I have used, the keys are arranged so that the keys are staggered a small increment to the left from the previous row. Q is above and slightly to the left of A, and A is above and slightly to the left of Z. This pattern continues across the entire board. Case in point:    What is the motivation behind this design? I would think that a column layout would be easier to type on - and indeed, many ergonomic keyboards seem to go with a column layout, where Q is directly above A and so on. Print file content without the first and last lines Integral of Sinc Function Squared Over The Real Line I am trying to evaluate $$\int_{-\infty}^{\infty} \frac{\sin(x)^2}{x^2} dx $$ Would a contour work? I have tried using a contour but had no success. Thanks.  Edit: About 5 minutes after posting this question I suddenly realised how to solve it. Therefore, sorry about that. But thanks for all the answers anyways. Diagonalisation and characteristic polynomial Let $A\in M_3(\Bbb R)$ which is not a diagonal matrix. Let $P$ be a polynomial (in one variable), with real coefficients and of degree 3 such that $P(A) = 0$. Pick out the true statements:  a. $P = cP_A$ where $c \in\Bbb R$ and $P_A$ is the characteristic polynomial of $A$;  b. if $P$ has a complex root (i.e. a root with non-zero imaginary part), then $P = cP_A$, with $c$ and $P_A$ as above;  c. if $P$ has a complex root, then $A$ is diagonalizable over $\Bbb C$.  I guess b and c are true although I am unable to disprove a. Because A could satisfy $(X-A)$ but this is not a polynomial. Now if $P$ has a complex root, then its conjugate too is its root as the polynomial has  real coefficients. As we all know An odd degree polynomial has always a real root, what we have is three distinct roots. Since $A$ satisfies the polynomial the only difference between the characteristic polynomial and $P$ has to be a constant. How do I connect to a MSSQL database using Perl's DBI module in Windows? Ensure a burned DVD will work any dvd player? When I double-click to select text in GNOME Terminal, the selection stops at spaces but continues over hyphens:      Some of my filenames contain uncommon characters such as the  and are not selectable by double-clicking:    Is there a way to make double-click selection continue over these characters as well? How to choose a lens for my first DSLR? I am considering buying my first DSLR.  How do I know whether I need a 18-200 lens, 17-85, or 18-55? Or something else? I am writing a cover letter and CV using moderncv. Everything works fine so far, but the text in the cover letter is not justified. I think it is good that it is not hyphenated, but it would look much nicer if the text was justified.  Here is a minimal example:  \documentclass{moderncv} \moderncvstyle{classic}  \usepackage{lipsum} % just for dummy text  \firstname{John} \familyname{Doe}  \begin{document} \recipient{Prof.\ Dr.\ Foo Bar}{} \opening{Dear Professor Dr.\ Bar,} \closing{Yours sincerely,} \enclosure[Attached]{curriculum vit\ae}  \makelettertitle \lipsum[1] \makeletterclosing  \clearpage  \makecvtitle  \section{Education} \cventry{2009--present}{PhD Student}{here}{and}{there}{} \end{document} Induction and electromagnetic fields I've got a few questions on induction and electromagnetic fields. My current understanding of induction and electromagnetic fields is that, when electricity/current flows through a wire, it creates an electromagnetic field. If you twist that wire into a coil then you can concentrate that field. You can then induce current into a different coil by placing it inside of the electromagnetic field created by the first coil.  So here are my questions:  Q1. Does the electromagnetic field contain any energy?  EDITED QUESTION  Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?   Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?  Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?  Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.   Thank you to anyone who answers.  Edited Q2: So my original question (although asked poorly) still stands. Where does the current that gets induced in the secondary coil come from? How does the electricity transfer from the primary coil to the secondary? For example, is it taken from the stored energy in the e.m field? Does the field just act as a bridge between the 2 coils? Or do the 2 coils exchange e.m waves which carry the electricity that is being transferred from coil 1 to coil 2? Or is it none of these things and something completely different? Is there any problem if the last name prints first than the first name on an air ticket? Is there any problem if the last name prints first then the first name in international air ticket? Eclipse menus are cut off or don't show I'm using Ubuntu 13.10 (with JDK 1.7.0_45).  I've downloaded and uncompressed Eclipse Kepler for Java EE Developers.  The software menus are messed up. I didn't notice similar problems in other software.  When I click any menu in Eclipse, the drop-down seems to be "cut". Sometimes the drop-down shows, but the options are invisible.  I tried Eclipse Indigo, but the same problem occurs. I have used quite some time searching for a solution to my compile problem. The document worked fine untill yesterday. After adding some new references, compiling stoped working properly. I have however used latex only for a few months, so the error might be an easy fix.   My error code in the blg file is:    [836] Utils.pm:209&gt; ERROR - BibTeX subsystem:  C:\Users\andre\AppData\Local\Temp\yb9w7ETEpQ\thesisbiblo.bib_16800.utf8,  line 1375, syntax error: found ",", expected one of: number, name (entry  type, key, field, or macro name), end of entry ("}" or ")") or quoted string  ({...} or "...").    I have biber 2.11 and miktex 2.9 and thought it could have been the cache file as suggested in a previous thread with 2.11 versions, but it did not do the trick to delete that either.  Thanks  This is how my "main" document looks like:  \documentclass[man,12pt,a4paper,babel,english]{apa6}  \usepackage{babel,duomasterforside} \usepackage[utf8]{inputenc} \usepackage[hidelinks]{hyperref}  % Math syntax  \usepackage{siunitx} \usepackage{upgreek} \usepackage{gensymb} \usepackage{amsmath} \usepackage{mathtools} \DeclarePairedDelimiter{\abs}{\lvert}{\rvert}  % Figures \usepackage{graphicx} \graphicspath{{Figures/}} \usepackage{float} \usepackage{subcaption}  % Biblography and citing \usepackage[style=apa,backend=biber,sortcites=true,sorting=nyt,autocite=inline,uniquename=false]{biblatex} \addbibresource{thesisbiblo.bib}  % Frontpage \usepackage{pdfpages}   \begin{document}  % Frontpage      \includepdf[pages=1-]{titlepage.pdf}  % Abstract \input{Abstract} \newpage  % Table of contents \tableofcontents \newpage  % Document \input{Introduction.theory} \newpage \input{Methods} \newpage \input{Results} \newpage \input{Discussion} \newpage \input{Conclusion} \newpage  % References                         \printbibliography  \end{document} I noticed that the reputation from the main site carried over to meta on Gaming (at least the first upvote), I guess that doesn't work the other way around, right?  Is it then impossible to have a meta reputation higher than the site reputation? Line breaking with hyperref href with an underline in itemize I have a simple itemized list like the following MWE:  \documentclass[10pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \usepackage{hyperref} \usepackage{lmodern} \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} \usepackage{lipsum} \begin{document} \begin{itemize} \item \href{http://google.com}{[ID1]: \underline{\lipsum[1]}} \end{itemize} \end{document}   This unfortunately doesn't break the block of text as expected, as shown below:    How can I fix this item so it will line break properly? I have this, in D1:  =sum(D3:D)   I want D1 to always be the sum of the rest of column D (D2 is a header)  I sometimes move a row, from eg 8 to 3, and that causes D1 to change to sum(d4:d).    I want D1 to stay as my sum of the column. With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss &amp; Oli: We are making this the master question for all future "Will this work on &lt;insert random tablet/phone/device here&gt;?!" questions What is glue stretching? I had a question about dynamic vspaces () and there was a hint I should use a stretchable glue. Searching with Google didn't give me a helpful answer.  I would be glad, if someone can explain it and give me a simple example to understand how it works.