It isn't really complicated, but I just can't figure out how to do it. I have one set with objects, let's say they are numbers. I need to check all the possibilities of N groups (we can assume there are 3 groups, 9 objects in set), where order inside group doesn't matter ({1,2,3}, {2,1,3}, {3,2,1}, etc. are the same) and order of groups doesn't matter ([{1,2,3},{4,5,6}] is the same as [{5,4,6},{2,1,3}]).  I'm writing code in C#, but there really isn't anything I could show. The closest idea I had contained a lot of fors and ifs 😞
I want to write a function that takes an array of letters as an argument and a number of those letters to select.   Say you provide an array of 8 letters and want to select 3 letters from that. Then you should get:  8! / ((8 - 3)! * 3!) = 56   Arrays (or words) in return consisting of 3 letters each.
Link button in post editor escapes square brackets in code I have added the png transparent image with the setting and its not showing transparent black background is seen. I have the base color aluminum and i want to add that logo of png on to it. The image is black letter with transparent background why its showing in white letters and black background. May i know where im going wrong any suggestion or help. Selecting one every n frames from a video using ffmpeg How old is the word "prolly"? Prolly is given this definition at :     Clipped pronunciation of probably.   I was reading an interesting article today that  from 1947 and that surprised me. Unfortunately, I wasn't able to find a listed source for the claim. So how old is prolly? Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$ Show that   $$\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$$  this is so confusing. i have no idea how to even start. im thinking integration by parts but that doesnt seem right.  hope you guys can help!! I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example.   Do magnetic fields do work directly, or is it their induced electric fields that do work? How do the Chitauri "ships" propel themselves? In the 2012 The Avengers film, the Chitauri army arrives through the portal along with these big robot alien whale Chitauri dudes. Here's one chasing Iron Man:  These guys basically swim through the air like... giant robot alien whales. I don't see any means of propulsion. Other, more humanoid Chitauri soldiers fly around on things that seem to be mechanical &quot;speeders&quot; of sorts. What are these guys? Are they ships, creatures, or both? Is there an explanation anywhere in the Avengers universe for how they defy gravity and swim through the air? I'm trying to create a functioning sub theme of Omega 4.4. I've worked  with Drush before with it, but the site is on a host that I'm not administrator of. I've tried the  but not succeeded in executing the Omega Wizard. In short, the Omega Wizard may be extremely helpful, but I can't get it to work.   Next, I've tried to manually create a sub theme using the . However, the results of this is a theme catalogue in the Themes-folder, but the theme not showing up in Drupal. Perhaps I'm using the wrong instructions for the wrong version of Omega?  Anyhow, does anyone have instructions for how to install an Omega 4.4 sub theme manually for Drupal 7? Maximum and minimum distance of two points Consider six distinct points in a plane. Let $m$ and $M$ denote respectively the minimum and the maximum distance between any pair of points.  Show that $M/m \geqslant \sqrt{3}$. Could there be an eighth Horcrux? Let $(A,+,\cdot)$ be a unity ring with the property that if $x \in A$ and $x^2=0$ then $x=0$. Consider the set $M=\{a\in A | a^3=a\}$. Prove that:      a) $2a\in Z(A)$, $\forall a\in M$, where $Z(A)$ denotes the centre of the ring $A$;   b) $ab=ba$, $\forall a,b\in M$.   My attempts revolved around the fact that an idempotent element in a reduced ring is central. So, since for $a\in M$ we have that $(a^2)^2=a^2$, it follows that $a^2\in Z(A)$, $\forall a\in M$. The next thing I wanted to use in order to solve a) was that $Z(A)$ is a subring of $A$, so if I had proved that $(a+1)^2 \in Z(A)$, $\forall a\in M$, then we would have reached the desired conclusion. However, I couldn't prove this and I honestly doubt that it is true. Another idea that I had was to prove that $M$ is a subring of $A$. Of course, this didn't work out because I cannot even prove that $M$ is closed under addition. Again, I don't know if this is true and it most likely isn't. As for b), I think that a) should be of use, but I don't know how. It is a well-known problem that a ring with $x^3=x$ for any $x$ in that ring is commutative, but since $(M,+,\cdot)$ is almost definitely not a ring, this doesn't help. EDIT: Is there any chance that this question is simply wrong? I tended to believe this before asking it here too, but since nobody has made any progress on it until now I am even more inclined to think so. Existence in ZF of a set with countable power set Is it consistent with ZF for there to exist a set $S$ such that the power set $P(S)$ is countable? If so, what is the weakest form of the axiom of choice needed to prove that no such set exists? Php string not working in Wordpress Functions.php (trying to fetch 1st category for each blog that post appears in the sidebar) I am trying to fetch 1st category for each blog post that appears in the sidebar of any blogpost landing page. I tried multiple options to add the 2nd block code to the 1st block at the line &quot;.wp_get_post_categories ($post_id).&quot; but I could not find any solution. Please help me with that and if you need closer to the code just let me know. 1st Block $related_blog .=&quot;&lt;div class='related-blog'&gt;                             &lt;div class='row'&gt;                                 &lt;a href=&quot;.get_the_permalink().&quot;&gt;                                                                  &lt;div class='col-lg-4 col-md-4 col-xs-4 blog-image'&gt;                                         &lt;img src=&quot;.$image_related[0].&quot;&gt;                                     &lt;/div&gt;                                      &lt;div class='col-lg-8 col-md-8 col-xs-8 blog-text'&gt;                                         &lt;strong&gt;&lt;p class='related-blog-title'&gt;&quot;.get_the_title().&quot;&lt;/p&gt;&lt;/strong&gt;                                 &lt;/a&gt;                                 &lt;span class='related-blog-sidebar-content '&gt;&quot;.substr(get_the_content(),0,250).&quot;...&lt;/span&gt;                                                                  &lt;p class='related-blog-sidebar-category'&gt;                                 &quot;.wp_get_post_categories ($post_id).&quot;                                                                &lt;/p&gt;                                                                  &lt;a class='related-blog-sidebar-link' href=&quot;.get_the_permalink().&quot;&gt;Read More                                 &lt;/a&gt;                                      &lt;/div&gt;                             &lt;/div&gt;                         &lt;/div&gt;&quot;;  2nd Block &lt;?php $category = get_the_category(); ?&gt; &lt;a  href=&quot;&lt;?php echo get_category_link($category[0]-&gt;cat_ID); ?&gt; &quot;&gt; &lt;?php echo $category[0]-&gt;cat_name; ?&gt; &lt;/a&gt; iOS app 1.4.3, iOS 9.2.1  While viewing a post, the app somehow ended up in a state where it refuses to do much of anything.  What does work:   Swipe-scrolling vertically Jumping to the previous / next post using the up / down buttons    Everything else, though, has no effect:   Swipe-scrolling horizontally will not return to the previous view Tapping on a code block will not zoom to code-block view Tapping Delete button to delete a post will show a confirmation dialog, but saying yes will not cause deletion The Add Comment button brings up the text field, but I cannot type anything in it; I can only dismiss it None of the other buttons (Share, More, etc.) do anything Cannot view user profiles or revision history Tapping on links in a post or comment will not show a web page Tapping on a tag shows some visual feedback with a temporary color change, but doesn't do anything else   I still receive push notifications, but tapping on them doesn't take me anywhere. Centering \vdots in a system of many equations I have a system of equations with an arbitrary number of equations (k). I'd like to use \vdots to compactly describe the system, like so:  \begin{align*}   R(-1) &amp;= \sum_{i=1}^m A(i)R(i-1) \\   R(-2) &amp;= \sum_{i=1}^m A(i)R(i-2) \\         &amp;\vdots                    \\   R(-k) &amp;= \sum_{i=1}^m A(i)R(i-k) \end{align*}     I'd like the dots, however, to be centered with = or the entire equation. Is there an elegant way of centering a column or row with AMSMath? I'm currently using an unholy combination of whitespace operators (\; \, etc.) to get the job done. It is quite easy to calculate the total number of functions from a set $X$ with $m$ elements to a set $Y$ with $n$ elements ($n^{m}$), and also the total number of injective functions ($n^{\underline{m}}$, denoting the falling factorial). But I am thinking about how to calculate the total number of surjective functions $f\colon X \twoheadrightarrow Y $.  The way I thought of doing this is as follows: firstly, since all $n$ elements of the codomain $Y$ need to be mapped to, you choose any $n$ elements from the $m$ elements of the set $X$ to be mapped one-to-one with the $n$ elements of $Y$. This results in $n!$ possible pairings. But the number of ways of choosing $n$ elements from $m$ elements is $\frac{m!}{(m-n)!\,n!}$, so the total number of ways of matching $n$ elements in $X$ to be one-to-one with the $n$ elements of $Y$ is $\frac{m!}{(m-n)!\,n!} \times n! = \frac{m!}{(m-n)!}$.  Now we have 'covered' the codomain $Y$ with $n$ elements from $X$, the remaining unpaired $m-n$ elements from $X$ can be mapped to any of the elements of $Y$, so there are $n^{m-n}$ ways of doing this. Therefore I think that the total number of surjective functions should be $\frac{m!}{(m-n)!} \, n^{m-n}$.  Is this anything like correct or have I made a major mistake here? I have a homework question that asks     Find necessary and sufficient conditions on $1 \leq i &lt; j \leq n$ so that $(i \, j)$ and $(1 \, 2 \, \dotsc \, n)$ generate $S_n$.   Here is what I have done so far.  Call $c = (1 \, 2 \, \dotsc \, n)$.  I made the observation that $$ \overbrace{c c \dotsb c}^{n - j + 1} (i \, j) \overbrace{c^{-1} c^{-1} \dotsb c^{-1}}^{n - j + 1} = (1 + i - j + n \, 1). $$ Thus, $\langle (i \, j), c \rangle = \langle (1 \, i - j + n + 1), c \rangle$, so it suffices to look at $\langle (1 \, k), c \rangle$ for positive integers $2 \leq k \leq n$.  I've checked that, for the value $k=2$, $\langle (1 \, 2), c \rangle = S_n$.  This immediately implies $\langle (1 \, n), c \rangle = S_n$.  I suspect that no other values of $k$ will work, but am not sure how to prove it. I have a MySQL table with utf8 general ci collation. In the table, I can see two entries:  abad abád  I am using a query that looks like this:  SELECT *  FROM `words` WHERE `word` = 'abád'   The query result gives both words:  abad abád  Is there a way to indicate that I only want MySQL to find the accented word? I want the query to only return    abád    I have also tried this query:  SELECT *  FROM `words` WHERE BINARY `word` = 'abád'   It gives me no results. Thank you for the help. Is "Michael here" correct? I edit a lot of posts every day. I often run across posts with 'Hi' and 'Thanks' on the top and the bottom of the post respectively. I also run across things like:     --User   Should these items be removed during the editing of the post by an editor?