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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In how many ways can a 4-letter word be formed from the tagged by: swerve ##### This topic has 4 expert replies and 2 member replies ### Top Member ## In how many ways can a 4-letter word be formed from the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning. A. 36 B. 144 C. 288 D. 864 E. 1728 The OA is D Source: e-GMAT ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 swerve wrote: In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning. A. 36 B. 144 C. 288 D. 864 E. 1728 Source: e-GMAT $$?\,\,:\,\,\# \,\,4\,\,{\rm{distinct}}\,\,{\rm{letters}}\,\,\,\left\{ \matrix{ \,2\,\,{\rm{vowels}} \hfill \cr \,2\,\,{\rm{consonants}} \hfill \cr} \right.$$ $$?\,\,\, = \,\,\,\underbrace {C\left( {4,2} \right)}_{{\rm{for}}\,\,{\rm{vowels}}} \cdot \underbrace {C\left( {4,2} \right)}_{{\rm{for}}\,\,{\rm{consonants}}} \cdot \underbrace {\,\,{P_4}\,\,}_{{\rm{chosen}}\,4\,,\,\,{\rm{permutations}}}\,\,\, = \,\,\,{{4 \cdot 3} \over 2} \cdot {{4 \cdot 3} \over 2} \cdot 4!\,\,\, = \,\,\,6 \cdot 6 \cdot 24\,\,\, = \,\,\,864$$ The correct answer is therefore (D). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 swerve wrote: In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning. A. 36 B. 144 C. 288 D. 864 E. 1728 There are 4C2 = 6 ways to choose 2 vowels from 4 vowels, and similarly, there are 4C2 = 6 ways to choose 2 consonants from 4 consonants Therefore, there are 6 x 6 = 36 different words with a particular set of 2 vowels and 2 consonants. However, for each of these 36 words, since the 4 letters can be arranged in any order, there are a total of 4! x 36 = 24 x 36 = 864 6 words possible. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 329 messages Upvotes: 27 swerve wrote: In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning. A. 36 B. 144 C. 288 D. 864 E. 1728 The OA is D Source: e-GMAT BIDE....BODE...etc  ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi regor60, I agree that this prompt is poorly-worded. The "intent" is to ask for every 4-letter arrangement that fits the given restrictions, INCLUDING "words" that do not appear in the dictionary (re: arrangements that are not actually words). GMAT question-writers are far more specific with how they word their questions, so you won't face this type of ambiguity on Test Day. GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 329 messages Upvotes: 27 Rich.C@EMPOWERgmat.com wrote: Hi regor60, I agree that this prompt is poorly-worded. The "intent" is to ask for every 4-letter arrangement that fits the given restrictions, INCLUDING "words" that do not appear in the dictionary (re: arrangements that are not actually words). GMAT question-writers are far more specific with how they word their questions, so you won't face this type of ambiguity on Test Day. GMAT assassins aren't born, they're made, Rich Gotcha. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 swerve wrote: In how many ways can a 4-letter word be formed from the letters ABCDEFIO such that the word contains 2 vowels and 2 consonants? The letters cannot be repeated, and, the words can have no dictionary meaning. A. 36 B. 144 C. 288 D. 864 E. 1728 Alternate approach: Case 1: VVCC, where the first two letters are vowels and the last 2 letters are consonants Number of options for the first vowel = 4. (Any of the 4 vowels) Number of options for the second vowel = 3. (Any of the 3 remaining vowels) Number of options for the first consonant = 4. (Any of the 4 consonants) Number of options for the second consonant = 3. (Any of the 3 remaining consonants) To combine these options, we multiply: 4*3*4*3 = 144. Other cases: To account for every possible position for the two selected vowels and the two selected consonants, we must multiply the result above by the number of ways to arrange VVCC. The number of ways to arrange 4 distinct letters = 4!. But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be arranged. The reason: When identical elements swap positions, the arrangement does not change. Here, we must divide by 2! to account for VV and by another 2! to account for CC: 4!/(2!2!) = 6. Thus: Total number of possible words = 144 * 6 = 864. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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