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Senior Manager Joined: 31 Oct 2010 Status:Up again. Posts: 428 Concentration: Strategy, Operations GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 04 May 2011, 01:12
00:00 Question Stats: 60% (01:45) correct 40% (01:38) wrong based on 201 sessions Hide Show timer StatisticsOut of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? A. 210 Guys I've some concerns on this problem and I've put them under the spoiler. Please help me out!Thanks.. _________________ My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html GMAT Club Legend Joined: 11 Sep 2015 Posts: 6807 Location: Canada
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 22 Apr 2018, 05:38 gmatpapa wrote: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? A.
210 Take the task of creating 5-letter words and break it into stages. Stage 1: Select the 3 consonants to work with Stage 2: Select the 2 vowels to work with If anyone is interested, we have a video on calculating combinations (like 4C2) in your head - see below Stage 3: Take the 5 selected letters and arrange them. By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25,200 ways) Answer: C Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it. RELATED VIDEOS _________________ Brent Hanneson – Creator of gmatprepnow.com Manager Joined: 09 Aug 2010 Posts: 60 Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 04 May 2011, 06:40 Using 4 x 3 / (2 x 1) = 6, to select your vowels... just calculated the number of groupings. Example: a e If you take the ARRANGEMENT into account, a e But it's best to just get the possible number of grouping first which is 7C3 4C2 = 210. Then we arrange it by multiplying to 5!.. So as to allow consonants and vowels alternating... Ex. c d f e i This will allow c d e i f.. Alternating elements... Retired Moderator Joined: 16 Nov 2010 Posts: 1011 Location: United States (IN) Concentration: Strategy, Technology
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 04 May 2011, 06:53 7C3 * 4C2 * 5! (7 * 6 * 5)/3! * 4!/2!2! * 120 35 * 6 * 120 = 210 * 120 = 25200 I don't
understand what is need of arranging the 5 letters again, as 7C3*4C2 will do that already. Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Senior Manager Joined: 31 Oct 2010 Status:Up again. Posts: 428 Concentration: Strategy, Operations GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 04 May 2011, 07:16 subhashghosh wrote: 7C3 * 4C2 * 5! (7 * 6 * 5)/3! * 4!/2!2! * 120 35 * 6 * 120 = 210 * 120 = 25200 I don't understand what is need of arranging the 5 letters again, as 7C3*4C2 will do that already. Uh.. thanks I think I got it now.. Say for example, the first combination is "r t y u i" You can sure arrange it in 5! ways, and since this is a unique combination, alphabets can be arranged in 5! and still form words not contained in any of the other combinations.
Thanks for pointing out. great tip! My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html Senior Manager Joined: 01 Feb 2011 Posts: 393 Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 04 May 2011, 16:44 7c3*4c2*5! = 25200 Answer is C. Director Joined: 08 May 2009 Status:There is always something new !! Affiliations: PMI,QAI Global,eXampleCG Posts: 607 Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 04 May 2011, 18:32 5 letters in the word - hence 5! ways of arranging them. positions - - - - - Thus without actually multiplying one can deduce like this : 5! = 120 means the number is divisible by 3.D and E POE. Also, the number must have 2 zeros at the units and tens place, 120 and 6*5 = 30 is there. C is a perfect fit. Current Student Joined: 16 Jan 2019 Posts: 649 Location: India Concentration: General Management GMAT 1: 740 Q50 V40 WE:Sales (Other)
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 28 Jun 2019, 19:11 I think the question needs to mention that repetition of letters is not allowed Posted from my mobile device GMAT Club Legend Joined: 11 Sep 2015 Posts: 6807 Location: Canada
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 29 Jun 2019, 05:09 firas92 wrote: I think the question needs to mention that repetition of letters is not allowed Posted from my mobile device Agreed! Otherwise, words like AABBB would be allowed. Brent Hanneson – Creator of gmatprepnow.com RSM Erasmus Moderator Joined: 26 Mar 2013 Posts: 2549 Concentration: Operations, Strategy
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 29 Jun 2019, 10:36 GMATPrepNow wrote: firas92 wrote: I think the question needs to mention that repetition of letters is not allowed Posted from my mobile device Agreed! Otherwise, words like AABBB would be allowed. أHi GMATPrepNow Brent How will be the solution if repetition would allowed? what will change in way to solve it? Thanks in advance GMAT Club Legend Joined: 11 Sep 2015 Posts: 6807 Location: Canada
Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 30 Jun 2019, 06:37 Mo2men wrote: GMATPrepNow wrote: firas92 wrote: I think the question needs to mention that repetition of letters is not allowed Posted from my mobile device Agreed! Otherwise, words like AABBB would be allowed. أHi GMATPrepNow Brent How will be the solution if repetition would allowed? what will change in way to solve it? Thanks in advance That rewording would require us to consider many different cases: Phew! I'm already tired. Cheers,
Brent Hanneson – Creator of gmatprepnow.com VP Joined: 04 Aug 2010 Posts: 1232 Schools:Dartmouth College Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 31 Oct 2020, 07:31 Given the OA, the prompt should read as follows: gmatpapa wrote: Out of 7 DISTINCT consonants and 4 DISTINCT vowels, how many words of 3 consonants and 2 vowels can be formed, if no letter may appear in the word more than once? A. 210 One approach: From the 5 positions in the word, the number of ways to choose 3 positions for
the 3 consonants = 5C3 = \(\frac{5*4*3}{3*2*1} = 10\) Number of options for the first consonant = 7 (Any of the 7 consonants) To combine the options above, we multiply: _________________ Private tutor exclusively for the GMAT and GRE, with over 20 years of experience. As your tutor, I won't simply teach you how I would approach problems. Non-Human User Joined: 09 Sep 2013 Posts: 24390 Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 20 Dec 2021, 05:47 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your
profile area as well as via email. Re: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 [#permalink] 20 Dec 2021, 05:47 Moderators: Senior Moderator - Masters Forum 3086 posts How many words of 4 consonants and 4 vowels can be formed out of 8 vowels and 5 consonants?Detailed Solution
But all these five alphabets can permute among themselves = 5! ∴ The required result will be 40320.
How out of 7 consonants and 4 vowels words of three consonants and two vowels can be formed?Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is equal to? = 210. Number of groups, each having 3 consonants and 2 vowels = 210.
How many words of 2 consonants and 2 vowels can be formed from 5 consonants and 4 vowels?⇒ Number of ways selecting 2 consonants = (5 × 4 × 3!)/(2 × 1 × 3!) ∴ The total number of ways is 1440.
How many words can be formed by taking 3 consonants and vowels out of 5 consonants and 4 vowels?Required number of ways = (210 x 120) = 25200.
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