Help identifying the word(s?) that describe or define this description:
Word for "moving up one conceptual level"
A fleet of nine taxis is dispatched to three airports, in such a way that three go to airport A, five go to airport B and one goes to airport C.  If exactly three taxis are in need of repair. What is the probability that every airport receives one of the taxis requiring repairs.  My method was total number of ways is (9!)/(3!*5!*1!)= 504 (this is correct)  Now you have three groups and of every group one position is already filled. So: ....R, ..R, R So the numbers of ways to distribute the rest is: (6!)/(2!*4!)=15  But according to answer model of my professor, it should be 90. So I assume he says the number of ways of distrubiting these 3 broken cabs over the 3 spots is 3*2*1. But to me this seems wrong? The broken taxis don't differ so R(1)R(2)R(3) is same as R(2)R(1)R(3). If you standing at the airport A, it doesn't matter which of the broken cabs stands there? Can I run CAT5/6 cables parallel to electrical cables? Analytic continuation of a power series 2 Another Qual question here,  For the function $$\sum_{n=0}^\infty z^{2^n}$$,  Prove the following:  i) $f$ converges to a function analytic in the open unit disk $D$,  ii) $f(z) =z+f(z^2)$ and  iii) $f(z)$ can not be analytically continued past any point on the unit circle.  I can even see (ii) very easily, but I can not see how can I prove rigorously (i) and  (iii). Help please. I am trying to testfor a player holding a diamond sword named Notch's Legendary Sword. How can I do that? Who ever gets the best answer will be able to get the first look at my NEW adventure map! Clipping image with Basic (ArcView) level license of ArcGIS Desktop? Is there a way to trim a geo-referenced air photo to an irregularly shaped boundary?    I tried the clip tool shown in my attachment, but it didn't work.  It looks as though the output extent field requires a rectangularly shaped polygon as the clipping feature.    Can I even do this in ArcView?    I've never had a request to do anything like this before.        I do use Photoshop and other similar software packages.  I could just go in to an environment like this &amp; start painting everything outside of my boundary in white, but then I would have to come back in and geo-reference the image again, and it just strikes me that there must be a faster and easier way (even though I only have ArcView 9.3). Combinatorics Distribution - Number of integer solutions Concept Explanation I reading my textbook and I don't understand the concept of distributions or number of solutions to an equation.  It's explained that this problem is 1/4 types of sampling/distributions problems.  An example is provided to illustrate:     In how many ways can 4 identical jobs (indistinguishable balls) be distributed among 26 members (urns) without exclusion (since one member can do multiple jobs)?      A sample outcome might be:   $\text{_____________}$   |  A  |  B  |  C  |...|  Z  |    $\text{--------------------}$      $\text{_____________}$   |  o  | oo|    |   |    ||| o  |    $\text{_____________}$   |  A  |  B  |  C  |...  |  Z  |    $\text{--------------------}$      Thus, the question is reduced to, "How many $(26-1+4)$ letter words are there consisting of four circles and $(26-1)$ vertical lines?"  Therefore, the solution is:  $\binom{26-1+4}{4}$   I really don't understand why its $(26-1+4)$.  There's only 26 different spots or "urns" to place the 4 jobs.  Can someone please explain?    I looked through another text to try and understand and I found it explained as such:       There are $\binom{n+r-1}{r-1}$ distinct nonnegative integer valued vectors $(x_1,...,x_r$ satisfying the equation $(x_1 + ... + x_r = x_n$ for $x\ge0$. $\spadesuit$   How in the world are they deriving this?  For distinct positive integers I understand:  Assume I have 8 balls (n=8) and I have 3 urns (r=3): o^o^o^o^o^o^o^o, where o represents  a ball and ^ represents a place holder where an urn could be placed.  For this scenario:     There are $\binom{n-1}{r-1}$ distinct positive integer valued vectors $(x_1,...,x_n)$ satisfying the equation:  $x_1 + ... + x_n = n, x_i&gt;0, i=1,..,r$ $\clubsuit$   It's clear that I could have this specific case ooo|ooo|oo.  Here the bar represents a divide for the urn and you see I have 3 sections.  So that case is clear.  Can anyone please explain this problem to me?  I don't understand the nonnegative integer case.   Also, people who post tend to be crazy smart and explain things very in a complicated manner.  I'd appreciate it if it could be explained in layman's terms as much as possible.   Thank you!!! "Give him a box that everyone knows what it contains." File changed listener in Java I am struggling to convert .dwg to .shp, ideas? Any ideas as to how can I convert dwg to shp?  I tried Kosmo and gvSIG. gvSIG kind of worked but it seems like I lost information.. in addition everything was converted into lines, no polygons. I can manually recreate the polygons, but there must be a better program to do this conversion.  Ideas? How to handle a native OS (Ubuntu) file upload window in selenium webdriver with python? This is my first time here but I have already posted this question on SO. I keep getting solutions for Windows + Java and not for Linux or python for that matter.  I am using Selenium and Python to automate a file upload application for the past many hours but nothing helpful!   The HTML DOM structure for this file upload is an input tag with its type attribute value = 'file'. I know I can make use of the send_keys.   The problem is I am not supposed to use send_keys() (as per the question I am trying to solve). The assumption is there are other ways of doing it.  Can anyone suggest me alternative ways to upload the file? I do get solutions for windows but not for Linux(Ubuntu). I know there are applications/tools to automate GUI components like AutoIt but there is nothing for Linux close to AutoIt.  I can say I have done my homework to find a solution. Only after not finding anything useful, I am asking this question, please help! As expected, Nvidia drivers have reduced my customizations. I can't login to Unity 3D session. I can't find any content to help me to uninstall the driver and I don't know what to do as I have never uninstalled them before. Let $X$ be a locally compact metric space which is also $\sigma$-compact. Let $C_{c}(X)$ be the continuous functions on $f$ from $X$ to $\mathbb{R}$ with compact support. Is $C_{c}(X)$ separable?  My work so far:   If $X$ is a compact metric space, then by Urysohn's Lemma and Stone-Weierstrass, the continuous functions $C(X)$ on $X$ are separable and hence the result follows as $C_{c}(X) = C(X)$.  Suppose $X = \mathbb{R}$. Write $\mathbb{R} = \bigcup_{N  = 1}^{\infty}[-N, N]$. Let $f \in C_{c}(\mathbb{R})$. Then $f$ is supported on a compact set $K \subset [-N, N]$ for some $N$. Thus $C_{c}(\mathbb{R}) =\bigcup_{N = 1}^{\infty}C([-N, N])$. Each $C([-N, N])$ has a countable dense subset $\{\psi_{N, n}\}_{n = 1}^{\infty}$ and so $\bigcup_{N, n = 1}^{\infty}\{\psi_{N, n}\}$ is a countable dense subset of $C_{c}(\mathbb{R})$.  In the general case, $X = \bigcup_{i = 1}^{\infty}X_{i}$ where each $X_{i}$ is compact and $X_{1} \subset X_{2} \subset \cdots$. Let $f \in C_{c}(X)$. Then $f$ is supported on a compact set $K = \bigcup_{i = 1}^{\infty}K \cap X_{i}$. Is it still true that $C_{c}(X) = \bigcup_{i = 1}^{\infty}C(X_{i})$? How to get reflections from 3D to show up on real images Andrew Price released a nice tutorial on how to nicely put 3D objects on top of a real image:   I have seen images, such as this:  which have 3D elements over images and have actual reflections from the object showing up on the wet asphalt.  How can this effect be achieved using render passes (or any other way)?  Here is another example (from ): Formula Specific to Running User? I have a requirement where a certain field can be edited without the validations firing for a particular user. Now I tried to write rule like LastModifiedId != '005000000000000AAA' but the validation was still firing. Then I realized that until the record saves, the LastModifiedId does not change and the validations still fire, as the LastModifiedId would not be updated to the exempted User.   Is there any workaround or a way to check the Id of the User who is currently editing the record? Why is the time limit for editing comments 5 minutes? What is the reasoning behind this? Automatically generate thumbnails for all subfolders of a directory in Windows 7? Note: this is intended to be a canonical question about whether or not a spell or ability targets so there are multiple sub-questions.   Can Hexproof or Shroud save my creature from ? What about a  that was cast for it's Overload cost? Does shroud prevent me from using the Monstrosity ability of a creature, or from giving it more counters with Proliferate? Can I cast an Aura Enchantment on one of my creatures with Shroud, or an opponent's creature with Hexproof? Or can I use the Equip ability to attach an equipment to one of my creatures with Shroud? Will 's ability trigger when my opponent plays ? And will I have to sacrifice my  if my opponent casts ? Will Shroud or Hexproof prevent an opponent from choosing me with 's ability? Will Hexproof keep one of my creatures from being affected by ? If an Aura or Equipment is attached to a creature with Hexproof, does the Hexproof protect the attached permanent? Add warning when changing display name sudo: unable to resolve host   I think I need to edit the /etc/hosts file to make an entry for 127.0.1.1 PC name.  But how can I do that if I can't access sudo? It seems to have gone since I updated to 13.10.  I have tried nano, which still doesn't work. Example 4.21 in Baby Rudin: Why is the inverse of this function not continuous at this point? Here's Theorem 4.17 in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition:      Suppose $f$ is a continuous 1-1 mapping of a compact metric space $X$ onto a metric space $Y$. Then the inverse mapping $f^{-1}$ defined on $Y$ by $$ f^{-1}( f(x) ) = x \ \ \ \ \ \ \ ( x \in X ) $$ is a continuous mapping of $Y$ onto $X$.    Now in Example 4.21 Rudin illustrates that compactness of $X$ is essential in Theorem 4.17.   So here is Example 4.21:   Let $X$ be the half open interval $[0, 2 \pi )$ on the real line, and let $\mathbf{f}$ be the mapping of $X$ onto the circle $Y$ consisting of all points whose distance from the origin is $1$, given by $$ \mathbf{f}(t) = ( \cos t, \sin t ) \ \ \ \ \ \ ( 0 \leq t &lt; 2 \pi). $$ Then this function $\mathbf{f}$ is of course continuous and injective. But Rudin asserts that the inverse function is discontinuous at the point $(1, 0) = \mathbf{f}(0)$. How to demonstrate this fact rigorously?  So far in the book, Rudin has not discussed the functions $\cos$ and $\sin$. So can we come up with an example that uses only what Rudin has discussed?