I want to choose $r$ items from $n$ items while the order of selection is not important. Using combination definition, there are $\binom{n}{r}$ different ways I can do that. What if $r&gt;n$? I expect the answer should be $0$ but all programming functions I have been testing returns error. I was wondering from a mathematical point of view, $0$ is a correct answer?
I am working on parameter estimation and one of the estimators involves a summation of $_nC_k$ ($n$ choose $k$) expressions. For some iterations, I need to compute expressions like $_0C_1$, $_0C_2$, etc.  In general how do we compute $_nC_k$ when $n$ is less than $k$? Do we still use the formula $\frac{n!}{(n-k)!k!}$ and use the gamma function to compute the negative factorial?  Thanks!
The following code  number=1 if [[ $number =~ [0-9] ]] then   echo matched fi   works. If I try to use quotes in the regex, however, it stops:  number=1 if [[ $number =~ "[0-9]" ]] then   echo matched fi   I tried "\[0-9\]", too. What am I missing?  Funnily enough,  suggests this should work.  Bash version 3.2.39. Entries I can safely exclude doing backups The expected value of $1/(1+X)$ where $X$ has geometric distribution Let $X$ be a random variable with a geometric distribution with parameter $p$.       Calculate $\Bbb E[1/(1+X)]$   I've looked at answers online but still do not understand how to solve this.   Specifically, I do not understand how to to get from $$\frac{p}{1-p} \sum_{x=0}^\infty (1/(1+x))((1-p)^x+1)$$  to  $-p\ln(p)  /(1-p)$. How can I put a bit mask on /dev/zero so that I can get bytes other than zero? How can I put a bit mask on /dev/zero so that I can have a source not only for 0x00 but also for any byte between 0x01 and 0xFF? How best can I discover what is up with my electrical bill? This might be subjective, I don't know. However, it's a serious problem for me. My electrical bill is outrageous. It's three times as large as my next-door neighbor, and four or five times the size of my neighbor's across the street. It's worse in the summer (I live in central TX), but I've had the air conditioner inspected, and while the house is right at the maximum capacity for our unit, the unit should still be able to take care of the load. That also doesn't explain why our winter bills are larger than the comparables.  What I would like to do is check the amount of current drawn by each running appliance and calculate where all my money is going. I just don't know how to go about doing this. I've used git clone to make a local copy of a GitHub repository containing a  I'd like to use. The local copy contains all of the source for the program; but as a newbie to Ubuntu, I've no idea of what tools or steps are involved in compiling and installing the driver.   I'd really appreciate if anyone could provide a step-by-step guide? I have two screens on my Windows 8.1 computer (with Classic Shell Start Menu installed). The thing is that I would like to have the taskbar's  (where the clock and all the icons like Skype or Spotify are, at the right) on both of my screens, and not only on the primary one.  Could you help me ? I would like not to install a heavy and paid software like DisplayFusion. I'm using Ubuntu Maverick and Virtual Box 3+. I have Windows 7 Ultimate. The problem is that it doesn't detect USB drives in Windows 7, but USB peripherals (mouse + keybord) are working.  I followed , but I can't find the user group vboxusers. How can I continue? I would also like to upgrade to the latest version without any risk (without losing my virtual hard disk drive). Creaking from cranks/spindle. How to fix? Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$ Problem:   If $f(x)$ is continous at $x=0$, and $\lim\limits_{x\to 0} \dfrac{f(ax)-f(x)}{x}=b$, $a, b$ are constants and $|a|&gt;1$, prove that $f'(0)$ exists and $f'(0)=\dfrac{b}{a-1}$.   This approach is definitely wrong:    \begin{align} b&amp;=\lim_{x\to 0} \frac{f(ax)-f(x)}{x}\\ &amp;=\lim_{x\to 0} \frac{f(ax)-f(0)-(f(x)-f(0))}{x}\\ &amp;=af'(0)-f'(0)\\ &amp;=(a-1)f'(0) \end{align}  I will show you a case why this approach is wrong:     \[f(x)= \begin{cases} 1,&amp;x\neq0\\ 0,&amp;x=0 \end{cases}\]   $\lim_{x\to0}\dfrac{f(3x)-f(x)}{x}=\lim_{x\to0} \dfrac{1-1}{x}=0$   but $\lim_{x\to0}\dfrac{f(3x)}{x}=\infty$,$\lim_{x\to0}\dfrac{f(x)}{x}=\infty$   Does anyone know how to prove it? Thanks in advance! Book series about preparation for a war at the Singularity I am looking for a book series (almost certainly a trilogy) that starts with some humans in a space station being abducted by a small funny-looking alien and taken to a prison planet. They find out that the way space travel works is by creating copies of the passengers, and the originals remained on the space station. This is actually good for the aliens since they believe every sentient being will resurrect at the Singularity and will be forced to fight a battle, so the more the merrier.  The one other detail I remember is that the world economy has a rampant inflation, so people take any cash they have at the end of the day and buy 20th-century memorabilia that doesn't devalue as much. Is there a universal way to turn Windows 7 Aero desktop, all windows, etc into grayscale? I had an option to do this in Intel video drivers on my old laptop, now I have NVIDIA and don't know how to replicate this effect.   There might be a shader or filter that would cause Aero to render stuff into grayscale, but I was unable to find anything. Or must it be explicitly supported by video driver as a bonus? Prove that if $\mathcal P(A) \cup \mathcal P(B)= \mathcal P(A\cup B)$ then either $A \subseteq B$ or $B \subseteq A$. I have something like that  how do I convert this to a YouTube playlist? In my D&amp;D 5e campaign one of the PCs who's a wood elf started dating a dark elf, and as a result she got pregnant and she is about to give birth. One of the other players had their PC die and he is considering playing as the child of the couple.  My question is, which race is the child going to be? Does the intersection of two finite index subgroups have finite index? SQL Server equivalent to Oracle's CREATE OR REPLACE VIEW In Oracle, I can re-create a view with a single statement, as shown here:  CREATE OR REPLACE VIEW MY_VIEW AS SELECT SOME_FIELD FROM SOME_TABLE WHERE SOME_CONDITIONS   As the syntax implies, this will drop the old view and re-create it with whatever definition I've given.  Is there an equivalent in MSSQL (SQL Server 2005 or later) that will do the same thing? Delay answer downvote rep loss to voter to help hide voter's identity A while back, I posted an answer to SO, which was downvoted.  I wasn't sure who did it, but had a suspicion because I thought I had seen a particular user lose a reputation point.  When I deleted the answer, my suspicion was confirmed by a point gain in reputation by the particular user.  Now, I wasn't going to attempt any sort of retaliation (and did deserve the downvote) but this seems like it could lead to abuse.  My suggestion is to apply answer downvote rep loss/gain at a particular time of day, and not immediately after the vote or answer deletion. International TLD's vs. duplicate content I currently work at a pretty big website that has visitors from around the globe. My job is to help out on the SEO, and one thing we've been discussing lately is the use of international TLD's. The ones we use range between:   (partly) translated websites like .es and .de that serve most of the content in the country's language non-translated (english) websites for non-english languages (due to a lack of translations) like .ro and .cz english websites for english speaking countries with localized TLD's (.co.nz, .co.uk)   On one hand I really have the feeling this is causing a lot of duplicate content, especially for the last two categories of TLD's.   On the other hand though it seems a lot like country-specific TLD's tend to score a lot better in that country's Google. Would it be advisable to keep on using these domains, or should we canonicalize them all to the .com version? I am fairly new to Unity3D experience , but I have a very good knowledge of Java and Android development. I am really confused that if Java is at all needed for developing android applications? I read somewhere in Unity documentation that adding behaviour to objects in Unity requires use of scripts, and that unity only supports C# , .Net , and Boo scripts. Is there no use of Java at all?