What is the probability that from 23 at least people 2 people have their birthday on the same day. Assume that the year has 365 days and that all the birthday combinations have the same probability.   Can anyone solve this?
I was wondering if someone could critique my argument here. The problem is to find the probability where exactly 2 people in a room full of 23 people share the same birthday.  My argument is that there are 23 choose 2 ways times $\displaystyle \frac{1}{365^{2}}$ for 2 people to share the same birthday. But, we also have to consider the case involving 21 people who don't share the same birthday. This is just 365 permute 21 times $\displaystyle \frac{1}{365^{21}}$. To summarize:  $$\binom{23}{2} \frac{1}{365^2} \frac{1}{365^{21}} P\binom{365}{21}$$
Proving that a number with digits 1...9 in some order, ending in 5, is not a perfect square. If "x" is a 9 digit number , which contains digits from 1 to 9 which ends in 5 . Prove that it can't be a perfect square ( digits are not to be repeated).  Please suggest the solution of this question. Einstein equation  where $E$ is energy, $m$ mass, and $c$ the speed of light in vacuum. So does it mean objects without any mass does not posses energy for eg lights photons does not have mass but how can they posses energy Print to standard printer from Python? I know that hardly any information is passed to the PDF when a .tex file is compiled.  But is there a tool that can convert a PDF document back to (La)TeX? I remember watching this one show when I was a kid in the 80's/early 90's in Canada. It was a live-action show about these two kids and had some puppet/muppet-like characters, but it kind of had a dark/mysterious element to it. I can't remember too much about it except portions of some episodes, but the main characters were kids, and they had some mysterious artifact (kind of like a compass?) that took them to this other world where there were giants and other mysterious beings that we rarely saw. The two kids weren't the only one's going to this place either, they find out kids from all around the world that also had this same artifact (and they all fit together like a round puzzle?). I seem to recall that the giants in this other world were the ones who made the artifacts, and were dying/or in desperate need of the help of the kids.  A couple episodes I remember:   There was one where the leaves were falling, and the world was doomed to end as soon as the last leaf touched the ground, so they're trying to figure out how to prevent all the leaves from falling, but after a long and suspenseful episode (for a kid) the last leaf dramatically falls, but out of no where the main girl catches the leaf and saves the world (it was very exciting for my young self, and I remember being very impressed with the pretty girl for thinking to catch the leaf).     There was another episode where the kids meet these two old guys with long white hair (muppets) sullenly working in a mine/tunnel, they're in tattered old clothes working away with their pick axes or hammers and they are connected to each other at the beard. This long old white beard grows out of one of their faces right into the other's. The kids save the day by cutting the old guy's beard in the middle, freeing them from each other. They celebrate being free from their bonds and excitedly thank the kids, but after the kids leave they continue to work away, this time in much brighter spirits. Seemingly unbeknownst to them though, as they work, their beards slowly and subtly grow back together.   Anyone else remember this show? Always sort Recent Places by date modifed I want to clear all previous commands from the history of my server. I used history -c and it seems all things are cleared but when I ssh to the server, all the commands are still there.  How can I clear them permanently? I’ve run into a limitation in the cURL bindings for PHP. It appears there is no easy way to send the same multiple values for the same key for postfields. Most of the workarounds I have come across for this have involved creating the URL encoded post fields by hand tag=foo&amp;tag=bar&amp;tag=baz) instead of using the associative array version of CURLOPT_POSTFIELDS.  It seems like a pretty common thing to need to support so I feel like I must have missed something. Is this really the only way to handle multiple values for the same key?  While this workaround might be considered workable (if not really annoying), my main problem is that I need to be able to do multiple values for the same key and also support file upload. As far as I can tell, file upload more or less requires to use the associate arravy version of CURLOPT_POSTFIELDS. So I feel like I am stuck.  I have  about this problem in more detail on the cURL PHP mailing list in the hopes that someone there has some ideas about this.  Suggestions or hints on where I can look for more information on this are greatly appreciated! Searching for words in question titles I'm trying to search for questions that have specific words in their titles using the  search feature, but it seems that it does not return any search results.  Using this feature, I tried to search for questions on Stack Overflow with , but this search query returns no results.  Is it still possible to filter the search results based on words in question titles? What does `exec {STDIN}>&0` do? Application of Kolmogorov's Zero-One Law Most of the books I read, they only state some examples of tail events. One of them is  $[\sum_n X_n \ converges]$. My main problem is to show that this is indeed a tail event. Linear regression in a loglog-plot with fixed slope Goal: create a plot to compare the empirical convergence rate of a numerical method with the one expected from the theory.  Accordingly, given a loglog-plot, I would like to add the line which has a prescribed slope (in this case, the convergence of the method) and the best intercept to fit the data (e.g., in a least-square sense).  Question: how to do a linear regression with fixed slope in pgfplots?  What I have done so far is the following: (1) compute the regression line (of the logarithm of the quantities), (2) save the intercept, (3) plot the line with the slope expected from the theory and this intercept.  This is a good approximation of what I am looking for, provided the data are in agreement with the theory.  Thanks  MdFB I will be landing at New Delhi airport. The worth of new laptop  (Lenovo Yoga Idea Pad 13) is about $1000 and old one (Macbook Pro) is > 1 lakh INR. I want to leave the new laptop in India. I have a copy of bill with me but not the original bill. I want to know if I have risk of being charged with custom duty. How to install packages to external drive (and run them)? I am running Xenial 16.04 and looking to install packages to an external drive - my computer has a 32gb SSD so it would be very useful to me to be able to use an external drive.  In a quick search I found a framework called  which seems to be designed to package all dependencies for a program (chromium, GIMP, some python packages, etc), but haven't had time to look into it.   seems to be looking for the same solution I am.   Thanks, Chris Difference between Unity and GNOME I often come across the terms Unity and GNOME while reading about Ubuntu. I understand that Unity is the default desktop environment for Ubuntu. What is GNOME and how is it related to/different from Unity? Which is correct?        She was told that it was against the law to steal.      Or        She was told that it is against the law to steal.        Background information: The original context is that I was relating an incident via email, where my colleague told a customer that some of our actions were part of the organisation's policy. The policy is still valid, but the statement I used to relate the incident in my email went like this:    "Mr Jay was informed that it was our policy to do this."   And I received feedback that it should go like this instead:    "Mr Jay was informed that it is our policy to do this." Prove that $A+I$ is invertible if $A$ is nilpotent Possible Duplicate:          Given $A^{2012}=0$ prove that $A+I$ is invertible and find an expression for $(A+I)^{-1}$ in terms of $A$. ($I$ is the identity matrix). Short expression to convey "but consider the source" Windows Update Slow on Vista Update I was able to get Readiness Tool to run but not the update Now the reediness tool will not even run Security Essentials will run    I have legal Windows 7 to install Do you think that is safe bet to try?    Had some performance issue so I ran MalwareBytes and Security Essentials.     It found some malware that was successfully removed.    I was able to Update Security Essentials and I ran it again for safety and it found nothing additions.     The last successful Windows Update was 5 days ago     Checking for Updates has been running 6 hours CPU 100%  network 0%     Windows6.0-KB947821-v35-x86.mnu fails to install It is supposed to be a tool to address update problems   I fear the registry got hacked to prevent updates     What can I do?  I know Vista.  I got it free. Travelling to Italy without my spouse who is a UK citizen