Here is the problem:  Let M (the sum) be 10 and N (the number of numbers) be 4.  Some possible combinations are are (10, 0, 0, 0), (5, 3, 2, 0), (8, 1, 1, 0), (8, 2, 0, 0), (6, 2, 1, 1), etc.  How do I calculate the number of possible combinations?  Thanks for the help.
How to use the  method?  Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$,  where $x_i\in\mathbb{N}$.  Is this the correct time to apply the method?  This is being repurposed in an effort to cut down on duplicates, see here:     and here:
Proof of inequality using AM-GM inequality prove that $x^2 + y^2 + z^2 \ge xy + xz + yz$  I tried proving it the way I prove $x^2 + y^2 \ge 2xy$. But it just doesn't seem to work. I tried using AM-GM. Should I be using GM-HM or AM-HM? I really don't know what the problem is and I'd appreciate any help and a full proof explanation. Thanks. I have some programs running on start-up like . UAC prompts every time the Windows starts. How can I set a program to make sure that no intervening prompt would appear during start-up? Sylow Theorem Explanation The Sylow theorems say that all $p$-Sylow subgroups are conjugate.   Is that the only thing they are conjugate to? In other words could a $p$-Sylow subgroup also be conjugate to something that is not a $p$-Sylow group?   Or does the fact that every element with order dividing $p$ is in a $p$-Sylow group mean that that is never possible? How do I get the browser to reask me to integrate with a website? I'm using  and I accidentally clicked "No" when asked if I want to integrate with the website.  How can I have Firefox or Chrome reask me to integrate the site with Ubuntu? What's the best way to return multiple values from a function? I have a function where I need to do something to a string.  I need the function to return a boolean indicating whether or not the operation succeeded, and I also need to return the modified string.    In C#, I would use an out parameter for the string, but there is no equivalent in Python.  I'm still very new to Python and the only thing I can think of is to return a tuple with the boolean and modified string.  Related question: How to install ibus-avro in Ubuntu 16.04 LTS? I tried to install ibus-avro, using the procedure that applied in Ubuntu 14.04 LTS. This procedure does not work in Ubuntu 16.04 LTS. Is there any other procedure to install avro in my new version of Ubuntu? Regex for parsing directory and filename I'm trying to write a regex that will parse out the directory and filename of a fully qualified path using matching groups.  so...  /var/log/xyz/10032008.log   would recognize group 1 to be "/var/log/xyz" and group 2 to be "10032008.log"  Seems simple but I can't get the matching groups to work for the life of me.  NOTE:  As pointed out by some of the respondents this is probably not a good use of regular expressions.  Generally I'd prefer to use the file API of the language I was using.  What I'm actually trying to do is a little more complicated than this but would have been much more difficult to explain, so I chose a domain that everyone would be familiar with in order to most succinctly describe the root problem. How do I import a namespace in Razor View Page? Geometric intuition for the tensor product of vector spaces What does the term $\mathcal O(\epsilon^2)$ mean? Resize Move Partitions on Dual Boot System I would like to be able to adjust the partitions shown below. Specifically, I want to add an additional 10GB from the unallocated space to /dev/sda5 (Ubuntu install). I will then format the remaining unallocated space as NTFS so it can be shared data between Windows and Ubuntu.   I am unable to increase the size of /dev/sda5 - I am only able to shrink it.  Any assistance would be greately appreciated. I have a txt file which actually is a html source of some webpage. Inside that txt file there are various strings preceded by a "title=" tag.  e.g.   &lt;div id='UWTDivDomains_5_6_2_2'  title='Connectivity Framework'&gt;    I am interested in getting the text Connectivity Framework to be extraced and written to a separate file.  Like this, there are many such tags each having a different text after the title='some text here which i need to extract '  I want to extract all such instances of the text from the html source/txt file and write to a separate txt file. The text can contain lower case, upper case letters and number only. The length of each text string(in characters) will vary.  I am using PowerGrep for windows. Powergrep allows me to search a text file with regular expression inout. I tried using the search as        title='[a-zA-Z0-9]  It shows the correct matches, but it matches only first character of the string and writes only the first character of the text string matched to the second txt file, not all string.   I want all string to be matched and written to the second file.  What is the correct regular expression or way to do what i want to do, using powergrep?  -AD. Rendering of Favorite/Ignored Tags in Firefox I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then typically this is changed to fish density but I have still decided to use a Poisson GLM, which I hope is right.   model1 &lt;- glm(g_den ~ method + site + depth, poisson)   My 3 predictor variables are method, site and depth which I ordered as factors when I input them.   My response variables are grouper species richness, grouper density and the same for other fish groups. I am aware that density is not an integer and it is numerical data e.g 1.34849. I am now however getting this error:      In dpois(y, mu, log = TRUE) : non-integer x = 0.037500   I've been reading up and many people suggest using an offset, is this the most advisable thing to do? So first let me state my homework problem:  Let $X$ be a set, let $\{A_k\}$ be a sequence of subsets of $X$, let $B = \bigcup_{n=1}^{+\infty} \bigcap_{k=n}^{+\infty} A_k$, and let $C = \bigcap_{n=1}^{+\infty} \bigcup_{k=n}^{+\infty} A_k$. Show that (a) $\liminf_k\; {\xi_A}_{_k} = \xi_B$, and $(b)$ $\limsup_k \;{\chi_A}_{_k} = \chi_C.$  I know that, in the context I am familiar with, that $$\liminf_{k\rightarrow +\infty}\; X_k = \bigcup_{k=1}^{+\infty} \bigcap_{n=k}^{+\infty} X_n$$ and $$\limsup_{k\rightarrow +\infty}\;X_k = \bigcap_{k=1}^{+\infty} \bigcup_{n=k}^{+\infty} X_n.$$   I also know that the characteristics (indicator) function is defined as $\chi_A(x) = \begin{cases} 1, &amp; x \in A \\ 0, &amp; x \notin A .\end{cases} $  So I wrote out $B$ in some of its `glory': $B= (A_1 \cap A_2 \cap A_3 \cap \cdots) \cup (A_2 \cap A_3 \cap \cdots) \cup (A_3 \cap A_4 \cap \cdots) \cup \cdots$, and as the first argument is the smallest, with increasing size to the right, the last term in the expression for $B$ would be $B$, which would be the largest.  So if I replace the $X_k$'s above with $\chi$'s I still don't see how I can get the correct answer - though it looks pretty clear from the definition of $B$ and that of $\liminf$ being basically the same, except in this case for the $\chi$.  Any direction would be greatly appreciated. By the way, I have checked out  but I was somewhat confused by the topology, the meets/joins, etc.  Thanks much, Nate moderncv: How to control the length of cvitems and cvlines? Let's say that a player uses the ready action and says "If a character aims at me with a weapon, I'll use Teleport to move behind cover."  What happens? Does this work? If not, please cite the rules to explain why not. I was trying to install Lightworks 11.5.1 (amd64) on Ubuntu 14.04(amd64) but there's a notice: Dependency is not satisfiable: libtiff4. Is there anyway to solve this dependency issue?  Thanks in advance. Convert from MySQL datetime to another format with PHP There is a hint to show that if there were points in $\mathbb{Q}$, then there would exist $r,s, t \in \mathbb{Z}$ with $\gcd(r, t) = 1$ such that $2s^2 = t^4 - 17r^4$ , and then show that any prime dividing $s$ is a quadratic residue modulo $17$.  I'm stuck on the first bit - if you suppose $\left(\frac{a}{b}, \frac{c}{d}\right)$ is a point on the curve in $\mathbb{Q}$ (so $a, b, c, d \in \mathbb{Z}$) then you get to $2a^2d^4 = b^2c^4 - 17b^2d^4$, but I'm not sure where to go from here since you don't know that $b$ is a square?