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Problem Solving : Permutation and combination Problem 1 : In how many ways can the letter of the word PROPORTION be arranged by taking 4 letters at a time?

In how many ways can the letter of the word PROPORTION be arranged by taking 4 letters at a time? Solution: P R O P O R T I O N below I've wrote letters without repeated words and then how many times particular word repeated P R O T I N P R O         O Here (P, P) 2 P, (R, R) 2 R, and (O,O,O) 3 O from the question here we gonna select 4 words hence we have the following chance to select those 4 words Chance 1:   3 O and remaining 1 are different (That means (O,O,O)--> 3 word and (P,R,T,I,N) ---> 1 word from the 5) Chance 2:  two of same words and other two of the  same words (here (O,O,O), (T,T) and (P,P) out of 3 pairs we gonna select 2 pair of words ) Chance 3: Two of same words and other two are different words (here (O,O,O), (T,T) and (P,P) out of 3 pairs we gonna select 1 pair of word and other 2 word from (R, O, I, N, T) words consider P,P has been selected pair  ) Chance 4: All 4 are different ( here P, R, ...

MySQL failed to start on Linux. 0 upgraded, 0 newly installed, 0 to remove and 464 not upgraded.

root@ubuntu:~# sudo apt-get install mysql-server  Reading package lists... Done Building dependency tree        Reading state information... Done mysql-server is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 464 not upgraded. The above installation error appearing while I've try to install my sql server, so it shows that installation has been broken, so you need to remove all the my sql server logs which are partially installed on linux, then again install it as the following steps, apt-get purge mysql-server apt-get purge mysql-common rm -rf /var/log/mysql rm -rf /var/log/mysql.* rm -rf /var/lib/mysql rm -rf /etc/mysql # and then: apt-get install mysql-server --fix-missing --fix-broken"

fatal error function name must be a string in php

In this below PHP programming I came across the following error <?php $user_ip = $_SERVER('REMOTE_ADDR');  echo $user_ip; ?> it  gives the error output in browser as " fatal error function name must be a string  on line 2 " so after checking that code I used ('REMOTE_ADDR') instead of ['REMOTE_ADDR'] so this could be the error free coding <?php $user_ip = $_SERVER ['REMOTE_ADDR'];  echo $user_ip; ?> o/p 127.0.0.1

10 Amazingly Simple Tricks To Turn Your Brain Into A Powerful Thinking Machine

10 Amazingly Simple Tricks To Turn Your Brain Into A Powerful  Thinking Machine There are two basic principles to keep your brain healthy and sharp  as you age: variety and curiosity. When anything you do becomes  second nature, you need to make a change. If you can do the  crossword puzzle in your sleep, it's time for you to move on to a  new challenge in order to get the best workout for your brain.  Curiosity about the world around you, how it works and how you can  understand it will keep your brain working fast and efficiently. Use  the ideas below to help attain your quest for mental fitness.  1. Read a Book Pick a book on an entirely new subject. Read a novel set in Egypt.  Learn about economics. There are many excellent popular non-fiction  books that do a great job entertaining you while teaching about a  subject. Become an expert in something new each week. Branch out  from familiar reading topics. If you usuall...

Magic Square Box and others

In this post I'm going to include some pictures which I made my innovation General formula in my school days, My innovation projects named  " Generalized Starting number for odd numbered Magic Square Boxes " and you can view those pictures here.... I have participated in district level school competitions of Maths and Science Expo at Anderson Matriculation School, Kanchipuram and this is a material I have exhibited in that event on 2004 (on my 11th standard) and won third prize and before that no one innovated this formula. What is Magic Square Box? It's nothing but when some numbers arranged in matrix square format such as 3 row 3 column and 6 row 6 columns, when you gonna add some numbers in row wise or column wise or diagonal wise, you will get some unique result. Example  4  9  2 3  5  7 8  1  6 in that above example when add the numbers row wise or column wise or diagonal wise you get the unique result as 15. ...

How to download Youtube Playlist videos?

If you want to download youtube playlist videos simply follow these steps: 1. Open Mozila firefox web Browser, then click this link https://addons.mozilla.org/en-US/firefox/addon/video-downloadhelper/  and download the Addon called "Download Helper" 2. Go to any youtube playlist as you want to download all videos in that playlist  3. After select all the video links from that youtube playlist then Right click ( make sure that you've selected all videos in that playlist ) on the mouse then you can click the option "Download videos from youtube link(s)", that's it.   See the below youtube video for multiple videos download from download helper addon.