Tuesday, December 29

Permutation n Combination

This is one of the most dreaded topics that a candidate can face in the GMAT exam. But, there are limited patterns that are asked in GMAT and if we can master them then i don't think one will have any trouble in solving these type of questions on GMAT.

I just got hold of my notes and decided to share em with fellow bloggers {there are some good questions that i will paste at the end of this post}:

1 Permutation : Permutation means arrangement of things. The word arrangement is used, if the order of things is considered.

2. Combination: Combination means selection of things. The word selection is used, when the order of things has no importance.

3. Example: Suppose we have to form a number of consisting of three digits using the digits 1,2,3,4,

To form this number the digits have to be arranged. Different numbers will get formed depending upon the order in which we arrange the digits. This is an example of Permutation.

4. Now suppose that we have to make a team of 11 players out of 20 players, This is an example of combination, because the order of players in the team will not result in a change in the team. No matter in which order we list out the players the team will remain the same! For a different team to be formed at least one player will have to be changed.

5. nPr = n!/(n-r)!

6. Note : Factorial of negative-number is not defined. The expression  –3! has no meaning.
7. Number of permutations of n-thing, taken all at a time, in which ‘P’ are of one type, ‘g’ of them are of second-type, ‘r’ of them re of third-type, and rest are all different is given by :-

8. Circular permutations

(a) If clockwise and anti clock-wise orders are different, then total number of circular-permutations is given by  (n-1)!

(b) If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by (n-1)!/2!

Restricted – Permutations

9(a) Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is to be always included in each arrangement:

r*( n-1) P(r-1)

9(b) Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is never taken:
(n-1) P(r)

10. nCr = nC(n-r) {general formula}

11. Total number of ways of selecting one or more things out of n different things

nC1 + nC2 + nC3 + ------------- + nCn = 2^n - 1

12. Total number of ways of selecting ZERO or More things out of n different things

(nC0 + nC1 + -----------------nCn) = 2^n

13. (nC0 + nC1 + -----------------nCn) = 2^n {general formula}

14. Number of ways of selecting zero or more things from ‘n’ identical things is given by :- n+1

15. Number of ways of selecting one or more things from ‘p’ identical things of one type ‘q’ identical things of another type, ‘r’ identical things of the third type and ‘n’ different things is given by :

 (p+1) (q+1) (r+1)(2^n – 1)

Some good questions to apply the theory

Q How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?

Q How many numbers are there between 100 and 1000 such that atleast one of their digits is 6?

Q How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?

Q How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?

Q How many number of times will the digit '7' be written when listing the integers from 1 to 1000?

Q Badri has 9 pairs of dark Blue socks and 9 pairs of Black socks. He keeps them all in a same bag. If he picks out three socks at random what is the probability he will get a matching pair?

Q How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?

Q If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

Q When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?

Q There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?


Sarah from Accepted.com said...

Excellent tips and excellent break-down of the material. Thanks for sharing your notes!
Scroll down to the bottom of this page (http://www.accepted.com/mba/appwriting.aspx#gmat) and you'll find some additional free tips and resources on the GMAT.

Best of luck,
Sarah Pritzker

Blaze said...

Seeking help : Illuminati

Gave my GMAT yesterday and got 510 (V:21 Q:39) . but was perplexed as to how i got so low score. Though my preparation was not up to the mark but even then i deserved something better.

1> Before giving my final GMAT i had only given two test one from CRACK-GMAT and one from Knewton , which was in the range of 450 , and that was 3 months earlier .( I seriously feel the lack of MOCK prep test was the reason . )
2> I started studying from June 2009 and gave the exam in Dec 2009 but it was not a regular study with thorough prepapration only starting in Nov , DEc 09 .
3> Now starting with the individual preparation for the subjects
Rc : I was never good with RC since childhod but never prepared for the subject as i thought it would only cater to the grasping part of the comprehension so i did 10 RC questions from OG-11 and i always got 50% accuracy . and read books and magazine a lot from paper and from internet . and yes to admit it i found the RC in actual test to be tough for me to answer . It came as early as the 4th question .
SC : Always felt this is the most important part in GMAT as there are so many rules of English Grammar that are involved in SC questions . Read and understood everything from grammar book .
Completed Manhattan SC guide - All questions from OG-10 (Twice ) . Read from Spidey Notes , Amatuers guide to GMAT SC .
Completed OG -11 SC ( Once ) . Prepared my own notes for the Grammar Rules .
Still i think i am weak in Parallelism & Comparisons kind of SC questions . In actual GMAT i could answer most of the SC questions properly as was able to eliminate the rest of the 4 choices due to some Grammar rules

CR : most of my preparation was for CR . Completed OG - 11 (Twice )
Practiced from some notes which had 97 questions with answer explanations ( Twice - this particular doc file had all the difficult OG-11 questions + plus some extra questions which were not easy as well ) : Found the actual GMAT CR a bit tough on some ocassions . I think OG has a easy level of questions.

I had 1000 CR / SC but i did not practiced from that as i could not get the answer explanaton for those questions .

Problem Solving : Completed Numbers , Equations , Ratio , Avg , geometry , Probability , Combinations from Quantitative Study material and was fairly confident in solving simple problems with 2 / 3 step solution .
Data Sufficiency : Completed OG -11 (Twice With 80 % accuracy )
I felt the actual GMAT questions to be easy ,only for one DS 5th question i selected the option wrongly as i realised it after clicking the confirm button .

For both Verbal and QS section it boiled down to last 10 questions 10 mins .so had to take guess in the last 3-4 questions in each sections .

I have made my own notes extensively for SC , CR , PS and DS and i used to revise from it .

I sincerely hope that u can throw some light on my study pattern ( pinpoint the flaws) and if possible guide me in preparing for the next GMAT attempt with respect to the study material / test taking ability and the approach that i should take for each of the different subjects .

Thanks in advance

Braveheart said...

hii Blaze...sorry to hear that you could not get the score that you wanted...

you need to pull up your socks in both Quant as well as verbal section...

1. RC is very important dont neglect it...and merely reading the papers or magazines wont help you because these sources dont have questions to test your comprehension...

Read online magazines...this will familiarize you with variety of topics tested on the GMAT RC...

Can i have your mail id?? or drop me a blank mail at my mail id mentioned on this blog and i shall share some material with you and some tips to improve your test [performance....

would be tough to pour all my thoughts on this comment... :)

garima said...

Hi Braveheart,

I gave GMAT twice, though in the first attempt i scored 530 Q:38, V:20; in the second attempt i scored 580 Q:42, V:25

my main areas of weakness were- Permutation combination and RC. Also, could you please advice asto how and when should i give the mock test..i plan to give it a third and last attempt in June 2010.

Look foward to your valuable suggestions.


Braveheart said...

@garima --> good news is Permutation n combination do not carry a lot of weight in GMAT..bad news is u really need to master the RC if u want to ace in GMAT...again the good news is its easy to master RC...

can you pls share your e-mail id with me?? i will send across some good material that would help you in GMAT verbal and quant as well...

In SEarCh of Thy sELf said...


Thanks for quick reply...much appreciated.

My id is garimakapoorpr@gmail.com

Thanks once again,

Dinesh said...

Hi Braveheart,

Your blog is pretty cool. I came across it through Pagal guy and I am going through it now. My goal is to get 700 plus and I am writing GMAT in early May. I live in Illinois and any help from you would be greatly appreciated. My email is dineshjazz@gmail.com. Can you please share with me some of the material you used online??


Manju said...

Hello Braveheart

First of all..Congratulations on ur awesome score!!! Well, i did give my gmat and got a terrible score, dont even feel like mentioning it. It would be great if you could share ur materials. any help from you would be greatly appreciated. My email id: fc135@yahoo.com