How many different words can be formed by taking 4 letters out of the letters of word again with each word has to start with a?
Show
GMAT Club Daily PrepThank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.Customized we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice we will pick new questions that match your level based on your Timer History Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.Hello Guest!It appears that you are browsing the GMAT Club forum unregistered! Signing up is free, quick, and confidential. Join 700,000+ members and get the full benefits of GMAT ClubRegistration gives you:
and many more benefits!
Intern Joined: 29 Dec 2009 Posts: 35 Location: india How many words can be formed by taking 4 letters at a time out of the [#permalink] Updated on: 26 Feb 2019, 03:23
00:00 Question Stats: 21% (02:42) correct 79% (02:31) wrong based on 371 sessions Hide Show timer StatisticsHow many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. A. 756 Originally posted by jatt86 on 14 Apr 2010, 04:33. Added options. Math Expert Joined: 02 Sep 2009 Posts: 86800 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 14 Apr 2010, 05:45 jatt86 wrote: 1) how many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter). Selected 4 letters can have following 3 patterns: 1. abcd - all 4 letters are different: 2. aabb - from 4 letters 2 are the same
and other 2 are also the same: 3. aabc - from 4 letters 2 are the same and other 2 are different: 1680+18+756=2454 Answer: 2454. Intern Joined: 07 Apr 2010 Posts: 19 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 14 Apr 2010, 06:40 a very similar question: Here we have 3 distinct letters(A,B,C) & 4 slots to fill. What logic do you use to solve this problem? Math Expert Joined: 02 Sep 2009 Posts: 86800 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 14 Apr 2010, 07:01 idiot wrote: a very similar question: Here we have 3 distinct letters(A,B,C) & 4 slots to fill. What logic do you use to solve this problem? Three patterns: 1. XXXX - only BBBB, so 1 1+18+36+8=63
Intern Joined: 07 Apr 2010 Posts: 19 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 14 Apr 2010, 10:41 thanks a ton, bunuel Manager Joined: 21 Mar 2010 Posts: 94 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 15 Apr 2010, 06:20 I'm usually not bad with anagram problems like this but the term "words" threw me off completely. MTHE - is hardly a word, so i started counting actual "words"... so obviously completely bombed the question! Manager
Joined: 14 Nov 2011 Posts: 105 Location: United States Concentration: General Management, Entrepreneurship GPA: 3.61 WE:Consulting (Manufacturing)
Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 25 May 2013, 17:50 Bunuel wrote: jatt86 wrote: 1) how many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter). Selected 4 letters can have following 3 patterns: 1. abcd - all 4 letters are different: 2. aabb -
from 4 letters 2 are the same and other 2 are also the same: 3. aabc - from 4 letters 2 are the same and other 2 are different: 1680+18+756=2454 Answer: 2454. Hi Bunnel, Math Expert Joined: 02 Sep 2009 Posts: 86800 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 26 May 2013, 03:13 cumulonimbus wrote: Bunuel wrote: jatt86 wrote: 1) how many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter). Selected 4 letters can have following 3 patterns: 1. abcd - all 4 letters are different: 2. aabb - from 4 letters 2 are the same and other 2 are also the same: 3. aabc - from 4 letters 2 are the same and other 2 are different: 1680+18+756=2454 Answer: 2454. Hi Bunnel, No, but this question is good to practice. Intern Joined: 22 Mar 2013 Posts: 8 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 02 Jul 2013, 10:45 Bunuel wrote: jatt86 wrote: 1) how many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter). Selected 4 letters can have following 3 patterns: 1. abcd - all 4 letters are different: 2. aabb -
from 4 letters 2 are the same and other 2 are also the same: 3. aabc - from 4 letters 2 are the same and other 2 are different: 1680+18+756=2454 Answer: 2454. Bunuel, this is a damn hard question and I find myself not fully able to understand your logic. I am from a very weak background but I have poured through all of the MGMAT math books (excluding the advanced one) several times and still find myself unable to intutively figure out the steps to this problem. What extra review would you suggest so I can be able to at least follow your solutions to these answers? Math Expert Joined: 02 Sep 2009 Posts: 86800 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 02 Jul 2013, 11:21 tmipanthers wrote: Bunuel wrote: jatt86 wrote: 1) how many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter). Selected 4 letters can have following 3 patterns: 1. abcd - all 4 letters are different: 2. aabb - from 4 letters 2 are the same and other 2 are also the same: 3. aabc - from 4 letters 2 are the same and other 2 are different: 1680+18+756=2454 Answer: 2454. Bunuel, this is a damn hard question and I find myself not fully able to understand your logic. I am from a very weak background but I have poured through all of the MGMAT math books (excluding the advanced one) several times and still find myself unable to intutively figure out the steps to this problem. What extra review would you suggest so I can be able to at least follow your solutions to these answers? This question is out of the scope of the GMAT, so I wouldn't worry about it too much. As for the recommendations. Best GMAT Books: best-gmat-math-prep-books-reviews-recommendations-77291.html Theory on Combinations: math-combinatorics-87345.html DS questions on Combinations: search.php?search_id=tag&tag_id=31 Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html Hope it helps. Intern Joined: 27 Mar 2013 Posts: 42 Location: United States Concentration: Strategy, Entrepreneurship GPA: 3.25 WE:General Management (Energy and Utilities)
Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 24 Mar 2014, 12:36 If this would have been a word with three of the same letter I'm assuming you would have more than 3 combinations? Thanks! Math Expert Joined: 02 Sep 2009 Posts: 86800 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 25 Mar 2014, 01:43 Mbearmann wrote: If this would have been a word with three of the same letter I'm assuming you would have more than 3 combinations? Thanks! Yes, we would have one more combination {a, a, a, b}. Intern Joined: 04 Apr 2015 Posts: 13 Concentration: Human Resources, Healthcare GMAT Date: 08-06-2015 GPA: 3.83 WE:Editorial and Writing (Journalism and Publishing)
Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 10 Jul 2015, 10:44 I can't understand this question. Why is this a combination question and not permutation? isnt it asking for arrangements? SVP Joined: 20 Mar 2014 Posts: 2426 Concentration: Finance, Strategy GMAT 1: 750 Q49 V44 GPA: 3.7 WE:Engineering (Aerospace and Defense)
Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 10 Jul 2015, 11:03 ddg wrote: I can't understand this question. Why is this a combination question and not permutation? isnt it asking for arrangements? You are half right. Permutations = Combinations * n! (where n is the number of 'elements'). In this question, you first need to select the letters out of the given one (combination implied as selection = combination!!) and only after you have selected the letters , you can look at the arrangements. You can not directly go to arrangements as you need to follow the 2 step process: 1. Choose 4 out of 11 letters Your approach would have been correct, had the question ask us to arrange all of these 11 letters into words of 11 letters or if all the letters were different. Intern Joined: 04 Apr 2015 Posts: 13 Concentration: Human Resources, Healthcare GMAT Date: 08-06-2015 GPA: 3.83 WE:Editorial and Writing (Journalism and Publishing)
Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 10 Jul 2015, 12:24 Thanks! this helpedGMAT Club Legend Joined: 03 Jun 2019 Posts: 4773 Location: India GMAT 1: 690 Q50 V34 WE:Engineering (Transportation)
Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 17 Aug 2019, 23:09 jatt86 wrote: How many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. A. 756 Asked: How many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. M-2 Words of the form abcd = \(^8C_4 * 4! = 1680\) Words of the form aabc = \(^3C_1*^7C_2* 4!/2! = 3*21*12 = 756\) Words of the form aabb = \(^3C_2 * 4!/2!/2! = 3* 24/4 = 18\) Number of words that can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS = 1680+756+18=2454 IMO E Kinshook Chaturvedi Senior Manager Joined: 30 Jun 2019 Posts: 286 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 24 Feb 2020, 15:39 I understand the solution, but where does this logic break down? (11*10*9*8)/(2!2!2!) = 990 Intern Joined: 25 Jan 2020 Posts: 1 Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 27 Feb 2020, 17:50 Bunuel wrote: jatt86 wrote: 1) how many words can be formed by taking 4 letters at a time out of the letters of the word MATHEMATICS. There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter). Selected 4 letters can have following 3 patterns: 1. abcd - all 4 letters are different: 2. aabb -
from 4 letters 2 are the same and other 2 are also the same: 3. aabc - from 4 letters 2 are the same and other 2 are different: 1680+18+756=2454 Answer: 2454. hey! Why are we taking 4C2 in the aabb combination? If we are looking to calculate how the letters are arranged, shouldn't we be using 4P2 instead? Thanks Re: How many words can be formed by taking 4 letters at a time out of the [#permalink] 27 Feb 2020, 17:50 Moderators: Senior Moderator - Masters Forum 3086 posts How many different words can be formed by taking 4 letters from the word again?The answer will be 1663200. How many different words can be formed by taking four letters out of letters of the word 'again' if each word has to start with A?
How many 4 letter words can be formed using the letter of the word?Solution. ∴ 840 four-letter words can be formed when the repetition of letters is not allowed.
How many different words can be formed by taking 4 letters from the word arrange without replacement?Expert-verified answer
We have 8 distinct letters( M,A,T,H,E,I,C,S). We choose any 4 from this and then arrange it in 8P4 ways=1680 ways.
How many permutation of 4 letters can be made out of the letter of the word examination?∴ 2454 different permutations can be formed from the letter of the word EXAMINATION taken four at a time.
|