How many 5-card poker hands are there containing at least 3 of the 4 suits? There are 52 cards in a deck and 13 cards of each suit.  Please check over my work and point me in the right direction for the last 2 parts.   The first card can be any suit (out of 4) and any card (out of 13). So 4 × 13. The second card be be any suit (now out of 3) and any card (out of 13). So 3 × 13. The third card be be any suit (now out of 2) and any card (out of 13). So 2 × 13. I don't know how to find the possibilities for the fourth and fifth card.
How many 5-cards poker hands are there containing at least 3 of the 4 suits?  I don't how know how to properly handle this question.  There 13 ranks of each card, and 4 suits  My Attempt:  Begin with the first 3: C(13,3) X 4 ways to choose suits  Then pick last 3 cards of anything:  C(49,2)  My solution: 1,345,344  Thanks,
How to find $\lim_{n\to\infty}\frac{1!+2!+\cdots+n!}{n!}$? How do I identify an airport’s official free Wi-Fi network? While traveling in the Berlin Tegel airport (TXL), I wanted to get on Wi-Fi. I found three unsecured networks in addition to a number of password-protected networks.   _Free_TXL_WiFi airberlin Berlin Tegel Airport WiFi   I had no idea which of these were an official Wi-Fi network provided by the airport and which were provided by other people, potentially for malicious purposes like capturing my network traffic. Presumably the official one uses a captive portal to allow internet access.  Is there any way to determine which Wi-Fi network is the official one provided by the airport? Would airport staff such as at the ticketing booths know? Are there official lists available somewhere?  I’d like an answer that is applicable to airports generally, rather than specific to the Berlin Airport. Also, please don’t just give a blanket “don’t use any public Wi-Fi network” answer; I know there are risks associated with it, but sometimes it is a necessity and so I want to know how to identify the airport-provided one.   suggests there are no official Wi-Fi networks, but the answers are six years old, so it’s not clear if things have changed or if none of the networks I saw were official. Is there an easy way of getting the charset and collation of the DB tables in WordPress without resorting to SQL queries? do_shortcode() within Admin Page I'm using a few plugins that have shortcodes ... however, instead of creating a public page for the content, I've created some new pages within the admin using add_menu_page and I need to know how to utilize do_shortcode() within this context.  As it stands, all the function does it spit out the string. I'm assuming it's because the shortcode API isn't available within an admin page.  How do I get around this? There is no documentation that I can find that explains how to utilize shortcodes within the WP Admin... or if it's even possible.    Specifically I'm trying to utilize WooCommerce shortcodes within the WP Admin. I hate the fact that plugins don't utilize the WP Backend for account/user management. TeXstudio does a pretty good job with autocompletion. For example, when I type \eqref{, it already comes with suggestions, see the example below.    However, suppose that I don't want to use \eqref but a customized command using newcommand (I do this so that I can quickly switch to different styles, e.g., some for journals/conferences "Eq. (1)" is needed, whereas sometimes "(1)" suffices). In this case, TeXstudio does not do the auto-completion, see the example below.    Is it possible to configure TeXstudio such that it does the auto-completion for custom commands that require a reference?  Note that one option is to redefine \eqref using \renewcommand, but I'm looking for another way so that I can use if for many more commands, not just for \eqref.   Here is my MWE:  \documentclass{article} \usepackage{amsmath}  \newcommand{\alternative}[1]{Eq.~(\ref{#1})}  \begin{document}     \begin{equation}         \label{eq:emc2}         E = mc^2     \end{equation}     I can refer to the equation using \eqref{eq:emc2} and using \alternative{eq:emc2}. \end{document} ArcMap Attribute Table not seen when second screen disconnected from Main Computer? I want to get a 360 and don't know wether to get the bigger (250GB), newer, more expensive Elite, or get one of the older, smaller (120GB), last gen ones. I know the arcade is going to be too small to save anything useful  How much hard disk space is recommend? What else is stored besides games? SQL Server 2014 - Strange SP behavior during compilation How to select records with maximum values in two columns? Upgrading straight handlebars to drop handlebars I have a two-and-a-half year old  (with a road-bike-like frame and thin tires; it's somewhere in the loosely-defined "hybrid" range) that I use to commute to work, twenty-five miles round-trip, once or twice a week. The bike has straight handlebars, and having gotten used to the idea of commuting via bike, I'm interested in upgrading to drop handlebars. It looks like I'd need new break/shift levers to go with the handlebars; the whole upgrade looks like it'd run a couple hundred dollars. This is a sizable fraction of the original cost of the bike, which leads me to wonder if I'm better off saving my money for a new bike that's a little better adapted to my use.  Is upgrading my bike's handlebars a reasonable investment? Showing that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$ Show that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$.   My reasoning is as follows:  Since the only ways $X^2$ and $X^3$ can be factored in $K[X^2,X^3]$ are $X^2 = X^2 * 1$ and $X^3=X^3*1$ it follows that $X^2$ and $X^3$ are irreducible.  To show that they are not prime in $K[X^2,X^3]$ I argue that $X^2\mid X^3*X^3$ but $X^2\nmid X^3$ and $X^3\mid X^4*X^2$ but $X^3\nmid X^4$ or $X^3\nmid X^2$.  Is that correct? "Optimiser" vs "optimizer"? I have seen words which are spelled either with a "z" or with a "s"  like "optimizer" and " optimiser".  I thought that the ones with "z" are wrong but on searching the web I found that both are correct. Why so? Is there any difference in the use also? How to have a one-to-many relationship with a privileged child? How does Latex compilers integrate packages into its existing core functions? what is the [count=\i] in \foreach for? Can someone explain what does [count=\i] in a foreach mean?  Antal S-Z's answer to  use this. It is also mentioned in , but I am not able to locate documentation on this in the TikZ-PGF manual (V2.10) Passing variable arguments to another function that accepts a variable argument list Changing Vim indentation behavior by file type Could someone explain to me in simple terms the easiest way to change the indentation behavior of Vim based on the file type? For instance, if I open a Python file it should indent with 2 spaces, but if I open a Powershell script it should use 4 spaces. Seeking podcasts related to geospatial technologies? I would like to make a list of podcasts related to geospatial technologies.  Do you listen to any that you find interesting and informative? Why did the texture I painted in texture paint mode disappear? I was following a  on how to use the Texture Paint feature on blender so I could paint on a terrain I am modeling. I was successful to paint the whole terrain with beautiful, exuberant vegetation, and crystalline water running through the valley.  So I saved my file, and I went to sleep. But now I've reopened the file and everything seems like I left it yesterday, except that I can see no texture in the terrain... The weird thing is that the textures i used are still there... I don't understand, I barely understand the interface, please help. I'm not even sure if the texture is there or if it was never "saved" or something...     I am now going through the second part of the tutorial for possible answers but I (and hopefully many more) will be grateful for your help. How do I (or can I) SELECT DISTINCT on multiple columns? I need to retrieve all rows from a table where 2 columns combined are all different. So I want all the sales that do not have any other sales that happened on the same day for the same price. The sales that are unique based on day and price will get updated to an active status.  So I'm thinking:  UPDATE sales SET status = 'ACTIVE' WHERE id IN (SELECT DISTINCT (saleprice, saledate), id, count(id)              FROM sales              HAVING count = 1)   But my brain hurts going any farther than that.