Given x and y denoting count of two different items, also given a value K. We need to select a total of K items from those X+Y items such that the count of chosen X items is odd. For example, X=4,Y=3,K=3. then number of ways= (4C1)(3C2)+(4C3)(3C0) here nCr denotes n!/(r!*(n-r)!) Is there any formula to calculate this?
How do I simplify: $$\sum_{r = 0}^{\lfloor \frac{k}{2} \rfloor} \dbinom{k}{2r} \cdot \dbinom{n-k}{k-2r}?$$ Basically, the sum is: $\dbinom{k}{0} \cdot \dbinom{n-k}{k} + \dbinom{k}{2} \cdot \dbinom{n-k}{k-2} + \dbinom{k}{4} \cdot \dbinom{n-k}{k-4} \cdots.$ This seems very similar to Vandermonde's Identity but because we skip two everytime instead of one, I don't see how I can apply it to this problem.
Server only reachable over VPN I have an Apache server running on a Raspberry P and it works just fine in the local network. And after forwarding port 80 and trying to connect using the public IP, Chrome says ERR_CONNECTION_REFUSED. But the strange thing is that I CAN reach the server when using VPN and using the same IP. What can I do?     -telnet 80.***.***.78 80      Trying 80.***.***.78...     telnet: connect to address 80.***.***.78: Connection refused     telnet: Unable to connect to remote host     -route -n      Destination     Gateway         Genmask         Flags Metric Ref    Use Iface     0.0.0.0         192.168.0.1     0.0.0.0         UG    0      0        0 eth0     192.168.0.0     0.0.0.0         255.255.255.0   U     0      0        0 eth0      -sudo netstat -lapute:              Active Internet connections (servers and established)     Proto Recv-Q Send-Q Local Address           Foreign Address         State       User       Inode       PID/Program name     tcp        0      0 *:http                  *:*                     LISTEN      root       6137        2051/apache2     tcp        0      0 *:ssh                   *:*                     LISTEN      root       6367        2249/sshd     tcp        0      0 pi.local:ssh            nmb.local:65535         ESTABLISHED root       8669        2565/sshd: pi [priv     udp        0      0 *:9949                  *:*                                 root       5918        1809/dhclient     udp        0      0 *:mdns                  *:*                                 avahi      6293        2184/avahi-daemon:     udp        0      0 *:54070                 *:*                                 avahi      6295        2184/avahi-daemon:     udp        0      0 *:bootpc                *:*                                 root       5946        1809/dhclient     udp        0      0 pi.local:ntp            *:*                                 root       6310        2200/ntpd     udp        0      0 localhost:ntp           *:*                                 root       6309        2200/ntpd     udp        0      0 *:ntp                   *:*                                 root       6304        2200/ntpd Difference between correlation and covariance: is covariance only useful if the relation is linear? I'm trying to understand better the difference between  covariance and correlation, besides the fact that the correlation coefficient is a dimensional and has values between $-1$ and $1$.   One unclear point is the following: the correlation coefficient can highlight only a linear relation between two variables, but does  covariance only work for linear relations too? Supposing that the relation is not linear, is the covariance not zero? Is it bigger than in the case in which the relation is linear?   Cauchy inequality says $$|\sigma_{xy}|&lt;\sigma_{x} \sigma_{y}$$  Which seems to say that the covariance is maximum when there is a perfect linear relation.    So I do not get what does happen if the relation is not linear, and, if covariance is not a suitable parameter in that cas I don't get the reason for that, since simply looking at the definition:  $$\sigma_{xy}=\frac{\sum(x-\bar{x})(y-\bar{y})}{N}$$  it looks like that this should be non zero for any kind of relation (like parabolic).  So can this be a difference between the use of covariance and correlation coefficient? (The first is useful for any kind of relation, the second one only for linear ones). Q&A blank in Stack Exchange Android app v1.0.95 - S10e/Android 10 Recently upgraded to a Samsung S10e and Android 10, but all Q&amp;A in the Stack Exchange app v1.0.95 are blank.  The title and comments are visible, but question/answer posts are just white space. Accessing the About page in the app is also blank.  I tried clearing data, cache and re-installing the app, but I still get the same behaviour. Equivalent of "both" when referring to three or more items? Can anyone tell me if I should use inspire or inspires in this phrase?     An extraordinary leader whose vision, values, integrity and boundless curiosity inspires all who follow in his footsteps. Can Recovery Mode install OS X onto a blank SSD? I want to install a new Solid State Drive (SSD) into the Mac. Can I just build in the SSD, start the MacBook in Recovery Mode and install OS X from there on?  After reading a lot on the internet I still have some doubts…  My HDD crashed, I can't repair it using disk utility or the fsck methods as mentioned on the internet.  According to  it should be possible.  I know how to replace the HDD with the SSD. I would go for the Samsung 850 EVO SSD - 500GB. My Mac is a MacBook Pro Mid 2012, model A1278. How to remove Apple System Apps How can I delete Apple OS X application such as Photos, iPhoto, and others that I never use? How can I obtain the command line arguments of another process?   Using static functions of the System.Diagnostics.Process class I can obtain a list of running processes, e.g. by name:  Process[] processList = Process.GetProcessesByName(processName);   However, there is no way to access the command line used to start this process. How would one do that? How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$? Let $a\geq 0$ and $ b\geq 0$. Prove that $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$. [Hint: Use the identity $(a^n -b^n)=(a-b)(\sum_{i=0}^{n-1}a^ib^{n-1-i})$]    I need some help! I cannot do it even with the hint... :( I'm a beginner at photography and own a Canon 20D with two lens; a 50mm prime and a 17mm-85mm zoom.  I've purchases all my filters at 67mm to fit my zoom lens and use a  to use them with my prime lens.  I'm looking at buying a . My question is, will the same principal work? Can I buy a 67mm wide angle lens and use it on my 52mm prime without any trouble.  One of the reasons for the purchase of a wide angle is my cropped sensor makes the 50mm prime rather close - I'm hoping the wide angle will make it easier to capture more.  Many thanks for any help in advance. Pete Via command line, I have a log file I'd like to keep track of.  What I want is to have, basically, a tail that refreshes when the log is updated making the text scroll upwards as new lines are appended to the log file.  Is there anything out there that does that without having to write some code? Do you ever center AND standardize variables in multiple regression? It seems as if standardization would automatically center variables...is this true? Which versions of C++ redistributables can I remove? I have a number of Microsoft Visual C++ 2005 and 2008 Redistributable and I would like to know which ones are safe to remove, because there are actually more than 10 installed on my computers.   Microsoft Visual C++ 2005 ATL Update kb973923 - x64 8.0.50727.4053 Microsoft Visual C++ 2005 Redistributable Microsoft Visual C++ 2005 (x64) Microsoft Visual C++ 2008 ATL Update kb973924 - x64 9.0.30729.4148 Microsoft Visual C++ 2008 Redistributable - x64 9.0.30729.17 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.17 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.4148 Microsoft Visual C++ 2008 Redistributable - x86 9.0.30729.4974 Microsoft Visual C++ 2010 x64 Runtime - 10.0.30319   It could be that these versions are all different, but a confirmation of that is fine for me as well. Thanks in advance.  PS. I'm using an x64 machine one windows 7. NSF IIS status date changed, status still pending I was working on a userscript today, which had a goal of displaying chat pings immediately at the main site. This would allow me to respond more quicker-like to chat pings.  However, I was met by this fearsome warrior:     Can we please set some decent header things? I want to be able to do this really bad. what is the [count=\i] in \foreach for? Can someone explain what does [count=\i] in a foreach mean?  Antal S-Z's answer to  use this. It is also mentioned in , but I am not able to locate documentation on this in the TikZ-PGF manual (V2.10) How do we prove that  $\operatorname{rank}(A) = \operatorname{rank}(AA^T) = \operatorname{rank}(A^TA)$ ?  Is it always true? What is the "canary thread" and why is it starving? Why do many sites leave half of each webpage empty? Isn't this a waste of screen space?  One nice example of this is the Stack Exchange Network sites:    As you can see, there is a ton of whitespace left on both sides of each page.  Does the whitespace make sites compatible with certain screen sizes? Does leaving the space help make sites mobile friendly? Does space make pages seem less crowded, and thus, more usable? Or, is there no good reason and people just do it because they don't realize they shouldn't?  I've worked on sites that use both designs and haven't had users complain either way.  Examples of sites that have space: , ,  Examples of sites without space: , , How do I instantiate a string array object into a Spring.Net container?