I was asked for the probability of having at least one card from each type (hearts/spades/etc.) in a 5 cards hand chosen randomly from a 52 cards normal deck. my solution was $\frac{{{13}\choose{1}}^4{{48}\choose{1}}}{{52}\choose{5}}$ as in, choose one card from each type and then one from the 48 cards left, then divide it all by all the possible hands. my solution is wrong, and I don't understand why, can someone please point out where have I gone wrong?
If each suit is represented then we will have two cards from one suit and one card each from the remaining suits. So I am counting the ways this can happen like so -  ${52 \choose 1}$ ways of selecting the first card.  ${12 \choose 1}$ ways of selecting a card from the same suit as the first.  ${13 \choose 1}$ ways of selecting a card for each of the 3 remaining suits.  So I have -  $${52 \choose 1}{12 \choose 1}{13 \choose 1}{13 \choose 1}{13 \choose 1}$$  Then I have the sample space as $52 P 5$ as we are counting with regard to order on the numerator so we need to do the same for the denominator.  So I have $$\frac{{52 \choose 1}{12 \choose 1}{13 \choose 1}{13 \choose 1}{13 \choose 1}}{52P5}$$  Does that look correct?
Why does the CAN bus use a 120 ohm resistor as the terminating resistor and not any other value? How is prototyping done in a professional EE environment? Do you do your prototypes on breadboards, on copper clad boards, Manhattan style, or do you just draw schematics, order PCBs made and assembled and work with them, hacking here and there if necessary? How do I switch to first person? We have a new application that requires glibc 2.4 (from gcc 4.1). The machine we have runs on has gcc 3.4.6.   We can not upgrade, and the application must be run on this machine.    We installed gcc 4.1, however, when it comes to compile time it is using all the includes, etc, from 3.4.6.    How do we get around this?  Any suggestions on using 4.1 for just this application? Sum of reciprocals of numbers with certain terms omitted I know that the harmonic series $1 + \frac12 + \frac13 + \frac14 + \cdots$ diverges. I also know that the sum of the inverse of prime numbers $\frac12 + \frac13 + \frac15 + \frac17 + \frac1{11} + \cdots$ diverges too, even if really slowly since it's $O(\log \log n)$.  But I think I read that if we consider the numbers whose decimal representation does not have a certain digit (say, 7) and sum the inverse of these numbers, the sum is finite (usually between 19 and 20, it depends from the missing digit). Does anybody know the result, and some way to prove that the sum is finite? Let users editing a question know if editing it would add it to the reopen queue This is sort of similar to , which was positively received, but was declined for technical reasons. I propose that users who are editing a post that was closed within the last five days be shown a notice on top of the edit form indicating that the post will be added to the reopen queue if edited, and that if one does not plan on editing the post into a state where it can be reopened, one should wait until five days after closure to make the edit. Closed questions are only added to the review queue once per closure by editing, and if a user comes by and makes a minor (yet benign) edit, the diff that reopen reviewers see is just that of the minor edit, and as such they dismiss the task as &quot;Leave Closed&quot;, which prevents it from being added to the queue again by another edit. This deprives the post author (and others interested in seeing the question reopened) of their chance to get the post reopened by editing. While some of these edits may be performed by users using (semi-)automated tools who would thus not see or overlook the warning, this will be a big help because 99%+ of users make edits solely manually and would thus see and possibly respond to such a notice. To help make this request more technically feasible, I propose that it instead only be loaded with the edit form, and that it should only be shown to users who can make binding edits. (Suggested edits occur at the time of approval, and the request to let the reviewers know has already been declined.) Here's an example of what I'm expecting:  This question was recently [closed/marked as duplicate]. This question will be added to a queue for possible reopening if you make this edit. If you are not planning to edit this post into a state where it can be reopened, please wait until [date and time after 70 days] to make your edit. If you are only making edits to the question's tags, please ignore this notice. Is there a way to merge to two bars in GNOME 3? Best case scenario would be to have one single bottom or top bar that has all the symbols on the left side and the rest like the time indicator, connections, on/off button, etc. on the right side.  Is that possible in any way? Opening Ubuntu 20.04 Desktop on WSL2 I installed Ubuntu 20.04 (server/terminal) from the Windows 10 app store, and then after launching the Ubuntu Terminal via WSL2 (Windows Subsystems for Linux) , I installed Ubuntu Desktop and did several steps to try and get a desktop instance of Ubuntu 20.04 launched.  In short, the steps involved editing the .bashrc file, installing Xming, and then attempting to open the Ubuntu desktop in Xming with the &quot;startxfce4&quot; command.  However, &quot;startxfce4&quot; just doesn't open the desktop for me.  I can get programs to open with &quot;grun&quot; and the file explorer to open with &quot;gopen&quot; though, so it is working partially. Does anyone have any alternative suggestions to how I might get the terminal to open up the full Ubuntu Desktop?  Obviously, this wasn't what Windows had in mind with WSL2 so this is kind of a reach, but any input would be helpful.  Could I somehow do this from the file explorer or with a program that could opened from &quot;grun&quot; or &quot;gopen&quot;? When to use ' (or quote) in Lisp? After making it through the major parts of an introductory Lisp book, I still couldn't understand what the special operator (quote) (or equivalent ') function does, yet this has been all over Lisp code that I've seen.    What does it do? Find $x$ in   $$ \Large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$$   A trick to solve this is to see that $$\large 2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}} \quad\implies\quad 2 = x^{\Big(x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}\Big)} = x^2 \quad\implies\quad x = \pm \sqrt{2} $$  Are these solutions correct? If not, why? If yes, are there other solutions?    PS: An extension of this discussion can be found in How to completely remove virtual packages? It turns out that removing a virtual package with apt-get only remove the package itself,  leaving behind the real packages that were installed by it  So how do you remove a virtual package, along with all the real packages that it installs? Blowing your own sail? How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation? Canonical Question  I want to do &lt;some really cool thing&gt; with a lightning:datatable, but I can't seem to figure out how to do it. I checked the , but I did not see a way to implement &lt;this really cool feature I need&gt;.  Perhaps I want to provide tooltips, or a pick list, or alter the behavior of the menus, or display images, or show a custom component I created, or define a new row-level click behavior, or alter the keyboard event handlers, etc.  Can I somehow do this? New tab in chromium is empty Note: I am very new to the more advanced side of electricity. I do not have a firm grasp on the exact mechanics.  Lets say I have an example circuit:  5V Power Supply -&gt; LED -&gt; Resistor -&gt; Ground  Now the LED is receiving 20ma and 5V. If I were to switch the LED and the resistor however, the LED should receive less voltage but the same current, so wouldn't it be dimmer? Or would it receive the same voltage?  I've looked at these two threads and their answer doesn't help. Interpretation of LASSO regression coefficients I'm currently working on building a predictive model for a binary outcome on a dataset with ~300 variables and 800 observations. I've read much on this site about the problems associated with stepwise regression and why not to use it.  I've been reading into LASSO regression and its ability for feature selection and have been successful in implementing it with the use of the "caret" package and "glmnet".   I am able to extract the coefficient of the model with the optimal lambda and alpha from "caret"; however, I'm unfamiliar with how to interpret the coefficients.    Are the LASSO coefficients interpreted in the same method as logistic regression? Would it be appropriate to use the features selected from LASSO in logistic regression?   EDIT  Interpretation of the coefficients, as in the exponentiated coefficients from the LASSO regression as the log odds for a 1 unit change in the coefficient while holding all other coefficients constant. steam fatal error "steam needs to be online to update, but was set to offline movies." I tried re-installing  it but it simply keeps giving me this error in a little window. When I close it, an identical error pops up some 3 seconds later without any new provocation. Is it possible to mark or modify a player with a specific item in their inventory I'm building a CTF map of sorts, using command blocks in vanilla 1.8. I've discovered two commands for detecting if an item is in a players inventory:  /clear @a[team=Red] banner 4 0  /testfor @a[team=Red] {Inventory:[{id:"minecraft:banner"}]}  Those work fine, unless you want to perform a command ON the player carrying that item. For example: I want to cause the player who picks up a banner of the opposite team, to automatically equip that banner in their head slot with a command similar to this:  /replaceitem entity @a[???????] slot.armor.head banner 1 4  Can this be done? If not, is there a way to mark a specific player carrying an item using scoreboards? Proper Installation of Kali linux tools in Ubuntu Me and some friends were recently disuccing "How cool it would be to be invisible", from a military viewpoint, I said that Camouflage, when done correctly, works surprisingly well, so invisibility was unnecessary. They countered with the argument that an infrared camera could see you easily. Apart from several warm coats, are there any non-restictive ways of preventing IR radiation being emitted from your person?