Permutation and Combination  
Dagny has been telling me
smugly that it's now my turn to write an article. So I decided to write one as
soon as possible and pass the buck back to her. We both know that it takes a
lot of pain to research for an article and write the text so we both try to
avoid it for as long as possible. On the other hand, since we both enjoy
writing and like to publish a wellfinished chapter, we both undertake the task
eagerly once the ball is in our court. Writing these chapters have made me
realize how true is the maxim "if you want to learn something well, teach it."
I can cite a lot of topics which I learnt while teaching in the class or
answering students' questions. These years of teaching have made so many topics
seem pretty childish to me which were nightmares to me before. But knowing a
topic well and teaching it are two different ball games. Many a times, I have
found myself struggling in the class to make a student understand something
which I have found obvious to understand! The fault is not on the student's
part. Three or four years ago, I would have been stuck on the same point! Every
time I encounter a situation like this, my only measure is to stop at that
point, retrace my steps with the students and slowly unravel the difficulty he's
facing. It works most of the times. But sometimes, the student is in so much
awe with the topic that his mind gets frozen. I have seen this happening many a
times. Topics such as time, speed and distance, Permutation and Combination, geometry etc. inspire so much fear among the
students that sometimes simple principles, which they would have otherwise
understood do not strike them as simple. I get incessant queries such as "Sir,
time speed distance chhod sakte hain?," "Sir, permutation combination na karein
to chalega?" from my students all the time. And the sad part is, that the level
of CAT in these topics is very simple. They are doable. In the present chapter,
I am trying to present one of these dreaded chapters as I understand it. I hope
my students understand it too. I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week. You might also like: Probability Maxima, Minima and Inequalities 
Re: Permutation and Combination  
Sir, Tatz a GEM OF AN ARTICLE thnkz, VaMsI 
Re: Permutation and Combination  
Now what do i say other than "THANKS A LOT TG !!! " u rock .... Amit 
Re: Permutation and Combination  
Very Very useful article.. Thanks 
Re: Permutation and Combination  
hey TG... awesome piece of writing dude... rather thanx dagny for giving him a push to write it... :D both of u all rock.. cheers, 
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TG Sir! Simply Fantabulous!! Just wanted to know do u have a Book having all topics of Quant...I have the book on Number theory which in itself, is very good.!!! 
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Thnks a lot TG........... i dont have word to say anything more ................... 
Re: Permutation and Combination  
THANKS A LOT TG!!! its a wonderful article..... 
Re: Permutation and Combination  
Thanks TG Awesome Article....... 
Re: Permutation and Combination  
Thanks a lot TG Doing a great job 
Re: Permutation and Combination  
Hi TG, The article is simply mind blowing!!!Plzzzzzzzz post an exercise on Permutation and Combination problems. 
Re: Permutation and Combination  
Is the answer to a+2b+3c.....total number of elements is 36? 
Re: Permutation and Combination  
Hi Rajdeep, About the exercise, have you seen the article completely? Total Gadha 
Re: Permutation and Combination  
Hi TG, That was an excellent article Can you please post some articles on functions,logarithms and probability 
Re: Permutation and Combination  
Hi Rakesh, Convert 24 to binary please? Total Gadha 
Re: Permutation and Combination  
TG/Dagny Wonderful work!!! I was going through the number system quiz,and have a doubt in a question .Where can I post my query ? Regards Arpita 
Re: Permutation and Combination  
Hi Answer is 630.give another try. 
Re: Permutation and Combination  
Hi Rudra, Corrected the typing error. And good way to solve the question. Total Gadha 
Re: Permutation and Combination  
Hi Tuhin, The second solution is correct. First has repetition. Please check the question of "three states with three students from each state...." Total Gadha 
Re: Permutation and Combination  
hi i'm here for the first time.. this was pretty helpful.. how do i cross check if i got the right answers?? will the solutions be available for the questions?? 
Re: Permutation and Combination  
Thank You for this very useful article. 
Re: Permutation and Combination  
That U Very much sir..........as expected my search for the best article on permutation and combination did end here.. 
Re: Permutation and Combination  
just being curious. are u vamsee krishna from CSE IITKGP, class 2006?? If you are kindly reply back, it would be nice to know one more familiar face at TG 
Re: Permutation and Combination  
Hi TG,
I haven't solved all the questions till now...just want to confirm the answers of first 5 ques.. 1 (a) 2(b) 3(d) 4. I m getting (26^3)*220 as my answer 5(c)

Re: Permutation and Combination  
Hi TG Sir, Please check the solutions pleazzzzzzzzzzzzzzz. I am waiting for solutions. Thanks and Regards, Manish 
Re: Permutation and Combination  
Frns
Check/discuss answers for above problems @ http://totalgadha.com/mod/forum/discuss.php?d=3683
VaMsI 
Re: Permutation and Combination  
Hi TG, Could you please post the complete solution to the Exercise. We are all eagerly waiting for it. Saurabh 
Re: Permutation and Combination  
Hi suren, I think the question involves just the selection. Hence the arrangement is not required. Hence 10c23c2=453=42 is the answer. 
Re: Permutation and Combination  
if the couples are siting at the ends the arangements are 2 X 2 X 2 x 6! Amit 
Re: Permutation and Combination  
Ya i agree with you sandesh, i too got this doubt.And i think we are correct. 
Re: Permutation and Combination  
(100)_{2} = 4 (in decimal) 
Re: Permutation and Combination  
hi TG, thanks,that was wat i thinking.... gr8 work .. Regards , sumit 
Re: Permutation and Combination  
Thats really a beautiful one. Made such a difficult task so simple with the examples of such a variety. Thanks a Lot Abnv

Re: Permutation and Combination  
Hi Randeep, 'Before' might not always mean 'just before,' as you have assumed by taking them together. There can be other persons between P, Q and R. Total Gadha 
Re: Permutation and Combination  
Hi Priyesh, There are four 4 even digits after removing zero 2, 4, 6 and 8. The number would end in one of these. Total Gadha 
Re: Permutation and Combination  
hi tg.. from where can i find the answers 2 the above exercise.. its v imp 2 chk whether i hav understud ur concepts pr nt. 
Re: Permutation and Combination  
hi sir, can u pls explain me the problem just before cicular combinations..i cant understand it clearly..pls help..thanks.. 
Re: Permutation and Combination  
hi sir this file is so good for cat exam so i want solution of the all prob so plz sand me the solution on my email 
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hey smruty, by any chance do you know the answer to your question? its coming out to be 72. if its correct i will tell you the procedure. 
Re: Permutation and Combination  
You r right. The solution given here, is based on a assumption that the three speek in order, which is not the case. Your solution is perfect i guess. 
Re: Permutation and Combination to Bheemesh K  
You r right. The solution given here, is based on a assumption that the three speek in order, which is not the case. Your solution is perfect i guess. 
Re: Permutation and Combination  
Hi TG.. Amazing article ..waiting eagerly for an article on Probability.. 
Re: Permutation and Combination  
Hi TG, A really helpful article,for it helped me revise P&C. thanks a lot. 
Re: Permutation and Combination  
@ ku klux klan You are forgetting to take one case into calculation The case is :  2 stay in same hotel and remaining 2 also stays in same hotel. 
Re: Permutation and Combination  
Hi sir .. its really superb.... thanks for ur article..... 
Re: Permutation and Combination  
TG STANDS FOR TRUE GUIDE........ 
Re: Permutation and Combination  
Thanx ashwin. U might think me to be a dud but kindly explain how u got the 2 in 2*5!*(6*5*4*3*2) . 
Re: Permutation and Combination  
Hi Saravanar, If first letter box posts even 1 letter or 2 letters etc. the second letter box does not have 10 ways. Total Gadha 
Re: Permutation and Combination  
Hi TG Thanks again, Wanted to share the probabilistic approach to dearrangement problem with the TGites. http://mathforum.org/library/drmath/view/56592.html A query: If you go through the proof in the link I have given, you can see that they are considering 4 out of 5 letters placed in the correct envelope. How come there result matches with the one given in this thread? I mean i could not find where I am going wrong. Please help!!! 
Re: Permutation and Combination  
6 Balls of different colours are to be distributed among 2 boys. What is the probability that each boy gets same number of balls? a) 5/16 b) 15/64 c) 1/2 d) 3/8 
Re: Permutation and Combination  
Hi Nishchal, You forgot the condition mentioned in the question every boy wants to sit with a girl. Total Gadha 
Re: Permutation and Combination  
in the condition mentioned by nischai every boy has at least one gal on his side!! 
Re: Permutation and Combination  
Hello TG sir, That's CAT like article on Perm Com......simplicity exemplified... Thanx Sir... 
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Hi TG Sir, can you please explain the solution for problem 3 
Answers  
1 a 2 b 3 d 4 c 5 c 6 a 7 d 8 c 9 c 10 b 11 b 12 c 13 14 a 15 16 17 b 18 d 19 a 20 c Please review and notify me for unattempted questions and wrong answers 
Re: Permutation and Combination  
agree wid siddharth n nischai. 
Re: Permutation and Combination  
Hi , reg question: how many ways can for persons be seated out of 5 boys and 3 girls on four different seats? why can't we go for ^{8}C_{4?} 
Re: Permutation and Combination  
There cant be a better article on P&C than this . 
Re: Permutation and Combination  
Hi Neelkamal
In the given example: it should be the desire of the girls also that they won't let two boys sit together otherwise your version is correct. Kamal Lohia 
Re: Permutation and Combination  
Hi Kamal, Can u pls post the answers to the problems mentioned above (P n C), otherwise how do i check which 1 is right n which 1 is wrong. Pls help. Thanks 
Re: Permutation and Combination  
Hi Nikita
In the numerator part there will be surely 5! and not 6! but why are you putting a 2 in denominator. Kindly express your thoughts. Kamal Lohia 
Re: Permutation and Combination  
Hi Destiny thanks for taking the time out. the book gives the answer as 6!/3!*3!*2 which works out to be 10. i am still pretty confused in this regard. 
Re: Permutation and Combination  
Hi Nikita I'm pretty sure that the answer is 3 and not 10. Did you get the logic I tried to explain in my last post??? 
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come on man solved all questions where is the solution I was highly disappointed after seeing no key 
Re: Permutation and Combination  
ketav , u can get ans here http://totalgadha.com/mod/forum/discuss.php?d=3683 
Re: Permutation and Combination  
very good elaboration of concepts..thanks a lot....!! 
Re: Permutation and Combination  
Hi Amit Please post the question statements here so that it becomes easier for everyone to try their hands at the problems. Kamal Lohia 
Re: Permutation and Combination  
Hi Amit What are the remaining possibilities for Q 27? Check. Kamal Lohia 
Re: Permutation and Combination  
Thank you Kamal sir for all your explainations. your way of explaination is awesome....simple and clear!!! I really appreciate your help. Regards, Amit 
Re: Permutation and Combination  
Hi Amit Gupta The problem is of repetitive counting. Try to check all the cases and find the repetition. Kamal Lohia 
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thank you kamal sir, I really didn't understood the question... thanks a lot... 
Re: Permutation and Combination  
Hi TG In how many ways six different faces of cube be painted in different color why cant answer be 6*5*4*3*2*1 
Re: Permutation and Combination  
but it is written six different faces 
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Clear explanation sir, thanks.. 
Thanks to all the authors nd contributing folks  
great work ...... But just one SHIKAYAT ..... We want more of these great articles Please find some time !!!!

Re: Permutation and Combination  
In the que where boys and girls go for spiderman movie why cant be there an arrangment gbbgbgbgbg still no girl is sitting together 
Re: Permutation and Combination  
Here, r+b+g=25 total ways=27c2=351 Now r 
Re: Permutation and Combination  
Hi Sumit, thanks for replying but I didnt got you.. where you got 27C2 from ? 
Re: Permutation and Combination  
Awesome article..no words.. 
Re: Permutation and Combination  
Hi Rachit Your answer and approach is correct. I'll fix it there. Kamal Lohia 
Re: Permutation and Combination  
(3^1/5 +7^1/8)^100 How many terms in the expansion are integers? 
Re: Permutation and Combination  
Hi Abheek You only need to find integral solution of the equation 5x + 8y = 100. And I am sure that you can do it easily. Kamal Lohia 
Re: Permutation and Combination  
hi TG thnx for such a wonderful article...please tell me if u posted any article on Integral Solution?? I couldn't find dat..pls hlp me in dat concept.. thnx 