You roll six independent fair dice.  What is the probability that their sum is divisible by 6?  I don't really know where to start. Does the ordering of the dice matter? (1,2,2,2,2,3) vs (3,2,2,2,2,1). I feel like it does. I'm not strong with counting arguments so I don't know how to find the number of ways that you can arrange that.
So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ideas?  Suppose that we roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by six?
"India has" or "India have" enumerate in multicols The following image illustrates what am looking for:    Essentially I want the numbering to occur as shown above but using the multicol and enumitem package. But when I try it by using the following code:  \documentclass{article} \usepackage{amsmath,amssymb} \usepackage{enumitem,multicol} \begin{document} \begin{enumerate} \item Evaluate each of the following if $x$ is a non-zero real number.     \begin{multicols}{2}     \begin{enumerate}[itemsep=1cm]% The item sep is my choice here.     \item $\dfrac{|x|}{x}$     \item $\dfrac{x}{|x|}$     \item $\dfrac{|-x|}{-x}$     \item $|x|-|-x|$     \end{enumerate}      \end{multicols} \end{enumerate} \end{document}   I get:    Essentially, I want the (b) to be where the (c) is. I know this has been done but I can't seem to find it. Can non basic lands be tapped for colorless mana? For example,  has a mana fixing ability, but it doesn't say you can tap it for mana. Other non-basic lands have a mana ability listed on the card. Should I assume that Evolving Winds cannot be tapped for mana?  Basic lands don't have mana tapping abilities listed, but are assumed you can tap them for mana of the color they represent. Calendar link to different page views We  that there's a difference in meaning between try used with the infinitive and  try used with the gerund:     I tried sending her flowers. (Meaning: An experiment: I sent her flowers to see what will happen).   I tried to send her flowers. (Meaning: I tried to go through the procedure necessary to send flowers to her. The procedure might have been difficult.)   (per Michael Swan's PEU, Unit 299.6)   Will the same distinction hold if we use trying:     A man is trying setting up a password on his computer. (Is he experimenting, wanting to see what will happen?)   A man is trying to set up a password on his computer. (Is he trying to go through all the necessary steps, probably difficult, of setting up a password?) Why must $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ -- the set of all polynomials in $\sqrt{2}$ and $\sqrt{3}$ with rational coefficients  -- contain multiplicative inverses?   I have gathered that every element of $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ takes form $a + b\sqrt{2} + c\sqrt{3} + d\sqrt{2}\sqrt{3}$ for some $a,b,c,d \in \mathbb{Q}$, and I have shown that $\mathbb{Q}[\sqrt{2}]$ and $\mathbb{Q}[\sqrt{3}]$ are both fields, but it's not clear to me why this allows for general multiplicative inverses to exist in $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$. is there any diffrence to use nonlinear or liner activation function in single hidden layer network Spambots causing server crashes. How do I block them? For example how come $\zeta(2)=\sum_{n=1}^{\infty}n^{-2}=\frac{\pi^2}{6}$. It seems counter intuitive that you can add numbers in $\mathbb{Q}$ and get an irrational number. Why does inertia happen? In  R P Feynman relates a story where his father told him that, even though we know the word "inertia" and what it means, nobody knows why inertia happens. Is that still true? Does kinetic friction increase as speed increases? Possible Duplicate:          Layman alert...I last did physics in high school, and am just trying to understand something my son is working on.   To keep a box moving across the floor at a constant velocity I need to apply a force equal and opposite to that of the  force working on it.  If I start applying a force greater than the kinetic friction force, the box will speed up. Will it keep speeding up indefinitely, or will the kinetic friction force I need to overcome increase as the box gets faster? :  Not ten minutes ago, I received this error, twice:  And also an &quot;Oops, something bad happened&quot; error.  I'm also getting question posting errors.  Can we fix this, please? Of course when you type:  sudo apt-get install whatever   It asks you:   Do you want to continue [Y/n]?    Is there any way I can just install it without it asking me if I want to continue? I don't really care about space, I have more then enough. In my book, it proves that an infinite subset of a coutnable set is countable. But not all the details are filled in, and I've tried to fill in all the details below. Could someone tell me if what I wrote below is valid?  Let $S$ be an infinite subset of a countable set $T$. Since $T$ is countable, there exists a bijection $f: \mathbb{N} \rightarrow T$. And $S \subseteq T = \{ f(n) \ | \ n \in \mathbb{N} \}$. Let $n_{1}$ be the smallest positive integer such that $f(n_{1}) \in S$. And continue where $n_{k}$ is the smallest positive integer greater than $n_{k-1}$ such that $f(n_{k}) \in S$. And because $S$ is infinite, we continue forever. Now consider the function $\beta : \mathbb{N} \rightarrow S$ which sends $k \rightarrow f(n_{k})$.   So in order for $S$ to be countable, $\beta$ would have to be a bijection. $\beta$ is injective since if $f(n_{k}) = f(n_{j})$, then $n_{k} = n_{j}$ because $f$ is injective. We also can conclude $k = j$ because the various $n_{i}$ chosen were strictly increasing.   Edit: $\beta$ also needs to be surjective. So for every $r \in S$ there exists a $q \in \mathbb{N}$ such that $\beta(q) = f(n_{q}) = r$. We know that $f^{-1}(r) \in \{n_{1}, n_{2}, ..., n_{k} ... \}$, so we can let $f^{-1}(r) = n_{d}$. Thus $\beta(d) = f(n_{d}) = r$. Regular expression to match DNS hostname or IP Address? Why can't I find the Karin Kuruma? Salesforce query on profile not working on user language change I have a query on profile like  profilename = [Select name from profile where id=:userinfo.getUserprofileid ].name  Now I have a check in  VF page  like  profilename  == 'System Administrator' . this works fine if the logged in user language is english. If the user language is different then profile name will be  'System admin' in that language . So how to prevent this beahviour?   Also  is there any particular field in profile which I can use  to identify the profile is system admin? so that I can have check on that field instead of checking for name which is causing the problem, for example I think modifyall filed is only checked for system admin. When using data.stackexchange.com I fail to remember if as [post link] is the correct alias to get the url for the post. Luckily the site has an  link. Unfortunately it is now broken. Can this be fixed? How do I stop Windows 10 from updating my graphics driver? How to use stars and bars for solving number of integral solutions to an equality? 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: