There are 5 tourists going to London. There are 7 places to visit in London. What is the probability that two attend one (same) location and 3 attend another (same) location.   So this is asking what is the probability that the 2 groups of people attend different places, but everyone from the groups is there. ex. $AB | C D E$ for the groups.  There are $\binom{5}{2}$ ways to choose 2 groups. There are $7^5$ total choices considering each person has seven choices.   There are $\binom{7}{2}$ ways to pick 2 locations from the 7.   Thus, $P = \frac{\binom{5}{2} \binom{7}{2}}{7^5}$  But the answer the book has is      $$P = \frac{7*6 \binom{5}{2}}{7^5}$$   Why are the locations suddenly distinguishable?
$5$ tourists plan to attend Octoberfest. Each attends a location at random from the choices: Alpine, Bingeman, Concordia, Kitchener, Queens, Schwaben, Transylvania. Q What is the probability that two attend one location and three attend another same location?  I get that there are $\binom{5}{2}$ possibilities to create 2 groups. There are $\binom{7}{2}$ ways to choose 2 places so shouldn't it be $\frac{\binom{7}{2}\binom{5}{2}}{7^5}$?
Travelling on Business visa to UK for tourism purposes Regular expression to match a line that doesn't contain a word I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "&lt;Regex for 'doesn't contain hede'&gt;" input   Desired output:  hoho hihi haha Proof of properties of injective and surjective functions. I'd like to see if these proofs are correct/have them critiqued.     Let $g: A \to B$ and $f: B \to C$ be functions.  Then:   (a) If $g$ and $f$ are one-to-one, then $f \circ g$ is one-to-one.   (b) If $g$ and $f$ are onto, then $f \circ g$ is onto.   (c) If $f \circ g$ is one-to-one, then $f$ is one-to-one?   (d) If $f \circ g$ is one-to-one, then $g$ is one-to-one?   (e) If $f \circ g$ is onto, then $f$ is onto?   (f) If $f \circ g$ is onto, then $g$ is onto?     (a)  Let $a,b \in A$.  If $(f \circ g)(a)=(f \circ g)(b)$, then $f(g(a))=f(g(b))$.  Since $f$ is one-to-one, we know that $g(a)=g(b)$.  And, since $g$ is one-to-one is must be that $a=b$.  Hence $f \circ g$ is one-to-one.    (b) Since $f$ is surjective we know that for all $c \in C$ there is a $b\in B$ such that $f(b)=c$.  Since $g$ is surjective, there is a $a \in A$ such that $g(a)=b$.  Hence, for all $c \in C$ there is an $a \in A$ such that $(f \circ g)(a)=f(g(a))=f(b)=c$.    (c)  This is false.  Let $A=\{1\}$, $B=\{1,2\}$, and $C=\{1\}$. Define $g(1)=1$ and $f(1)=f(2)=1$. Then $f \circ g$ is injective, but $f$ is not injective.    (d)  This is true.  Let $a,b \in A$ where $a \neq b$.  If $(f\circ g)(a)\neq(f\circ g)(b)$, then $f(g(a))\neq f(g(b))$.  Hence $g(a) \neq g(b)$.  (e)  Since $f \circ g$ is surjective, then for every $ c \in C$ there is an $a \in A$ such that $f(g(a))=c$.   Let $b = g(a)$.  Then $b \in B$ and $f(b)=g(f(a))=c$.  Thus $f(b)=c$.  Hence $f$ is surjective.  (f)  Using the same set up as part (c), we have that $g$ is not surjective since there is nothing in $A$ such that $g$ will go to 1. Why are naturals < modulus equal if congruent? [uniqueness of remainder] Let $a$, $b$, and $n$ be integers with $0 \le a \lt n$ and $0 \le b \lt n$. Suppose $a \equiv b \pmod n$. Then $a-b=0$ and $a=b$. Why does the congruence of two non negative integers imply that they must be equal? Coordinating conjunction immediately followed by parenthetical — Is a comma needed or not? states:     If a dependent clause, or an introductory phrase requiring to be set off by a comma, precedes the second independent clause, no comma is needed after the conjunction.   Strunk's example illustrates the point:     The situation is perilous, but if we are prepared to act promptly, there is still one chance of escape.   However, I would be tempted to put a comma after the "but," like this:     The situation is perilous, but, if we are prepared to act promptly, there is still one chance of escape.   So, I know you're thinking, "Well, Strunk's Rules of Usage says that you're wrong. No comma."   But is Rules of Usage really the best source? I'd like to see this rule in a more contemporary and authoritative source, like the Chicago Manual of Style.  There are many instances —  — where the comma is included before a parenthetical comment that comes after a coordinating conjunction.  Any authoritative source on the issue? Etymology for “Mc‑” and “O’‑” prefix in surnames There is clearly a prefix in names like McDonald, McChrystal, O’Brian, O’Neal.  What does this Mc- and O- prefix signify? It looks like Donald, Chrystal, Brian, Neal are perfectly fine names on their own, so why is there a prefix before it? How to turn off the iOS-style character picker menu House address is not listed on Google Maps When I search for my address on Google Maps it cannot be found which means I can't order takeaway etc.  Is there a way of adding my address to Google Maps or even add a street address?  I want the address to be publicly available so others can search it. Decrypt all RSA ciphertexts if you can break 1% of them I was given a cryptography question during an interview the other day.   Imagine you are given an efficient algorithm which for a given RSA public key (n,e) is able to decrypt 1% of the messages encrypted with that key.   1% means that the algorithm will deterministically decrypt 1% of all possible ciphertexts on the first call, and will never decrypt the other 99% of all possible ciphertexts with any number of invocations.   Figure out an algorithm that uses this one and can decrypt any message. Any ideas? inputenc Error: Unicode char \u8: not set up for use with LaTeX This is with ref to my previous question .  \documentclass[11pt,table,a4paper]{article} \usepackage{lmodern} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}  \usepackage{CJKutf8} \usepackage[english,russian]{babel}  \newenvironment{SChinese}{%  \CJKfamily{gbsn}%  \CJKtilde  \CJKnospace}{}   \begin{document}  \selectlanguage{russian}   Это мой первый многоязычный докладе.   Инфантильный гипертрофический стеноз привратника - это серьёзное   \selectlanguage{english}   This is my first multilingual report.   \begin{CJK}{UTF8}{}   \begin{SChinese}     这是我的第一个多语种的报告。   \end{SChinese}   \end{CJK}    \end{document}   when I try to compile it, I get following error message.  LaTeX Warning: Unused global option(s):     [table].  (./data.aux (/usr/local/texlive/2011/texmf-dist/tex/latex/cyrillic/t2acmr.fd)) (/usr/local/texlive/2011/texmf-dist/tex/latex/lm/t1lmr.fd)  LaTeX Font Warning: Font shape `T2A/lmr/m/n' undefined (Font)          using `T2A/cmr/m/n' instead on input line 15.   ! Package inputenc Error: Unicode char \u8:  not set up for use with LaTeX.  See the inputenc package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                      l.18 ...�ный гипертрофический стеноз привра...   How can I avoid such error message. Windows INSERT key anti-functionality accidentally triggers; how to stop it permanently? Is there a cleaner proof of convergence for this almost-telescoping series I was wondering how the convergence of the series $$\sum_{k\geq1}\frac{(k+1)^y-k^y}{k^x},$$ depends on $x$ and $y$, where $x$ and $y$ are real numbers. I've been able to show that it converges if and only if $y\leq x$, by distinguishing nine cases; whether $x$ and $x-y$ are positive, negative or zero. If desired I can include a sketch of my proof. My question is whether there is a proof that works for all real $x$ and $y$? Or at least a proof that seems less artificial? Is it possible to use NBT tags in commands in Minecraft: Bedrock Edition? This question was recently split into different questions for each workaround. See   meta posts for more information.   Can you use NBT tags in commands? I’ve tried commands that normally work in Java Edition like: give @s minecraft:planks 30 1 {display:{Lore:[&quot;Wooden planks&quot;]}} give @s stone_pickaxe{Unbreakable:1b} give @s item_frame{EntityTag:{Invisible:1b}} summon villager ~ ~ ~ {Offers:{Recipes:[{buy:{id:&quot;emerald&quot;,Count:5b},sell:{id:&quot;diamond_sword&quot;}}]}} summon tnt ~ ~ ~ {Fuse:20s} Books for Hyperbolic Geometry. I want to read hyperbolic geometry. Can any one suggest some good books on the topic. At what speed does our universe expand? I know this subject was discussed for many times, but I still don't get it..  I've read in a book that we can use "I've got" instead of "I have" for possesion and it gave some examples,      I've got an English book.   I've got a red car.   So I understand that it can be used only for possession of physical objects, but I saw it used in sentences like "I've got something to say", is it correct? I hope it's not a stupid question..Thank you very much! How do  I create a desktop wallpaper slideshow with my own set of images?   With the images coming from a pictures folder, or pre-selected With the images displayed in order, or randomly With the images changing every few minutes, or after random periods of time Bounded operator that does not attain its norm What is a bounded operator on a Hilbert space that does not attain its norm? An example in $L^2$ or $l^2$ would be preferred.  All of the simple examples I have looked at (the identity operator, the shift operator) attain their respective norms. Can magnets rotate infinitely? There are many videos on youtube in which people arranged magnets in circle and rotated one placing in middle of that circle on a shaft, and the magnet (magnet motor) starts madly and continues its movement. Do they really rotate infinitely? If so, do they from where they get that extra energy to move so fast and infinitely?    EDIT: This question is about real world scenario  UPDATE: I am unable to find that particular video about which i talked about -- I added them to my favourites, but they are all now deleted :( -- there are hundreds of that that kind of videos. Some example videos links I'm running the Storm King's Thunder campaign, and we are at the portion where the PCs get an airship to travel around in, the airship is about 1000ft in the air. There are approximately 5-6 lvl 7 PCs, and they have 3 or 4 hard encounters a day. There are two wizards, a warlock, ranger, paladin, blood hunter, sorcerer, and fighter. For the most part, they have had fun with the different weapons and enemies they have faced; however, I find that one or two spellcasting PCs have been using spells such as mind sliver, polymorph, and hypnotic pattern to defeat more challenging encounters, such as one with a roc and wyvern. They make the creature make saving throws with hypnotic pattern and cause the enemy to fall to its death, and using mind sliver makes it even harder, especially on low wisdom creatures like rocs. Or with the polymorph spell, they cause the enemy to become a fish or chicken and throw it off the edge, and since the damage carries over, it kills the monster. I realize it was legal and made fights funnier, but it does get annoying when it's happening in almost every fight. Are there any suggestions on how to keep them on track without them making every encounter easy? I thought of giving the monsters immunity to these effects, but it just sounds like a bad excuse for me not being prepared.