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how many words

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nahid078 Really wants to Beat The GMAT!
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how many words Post Mon Sep 08, 2014 4:22 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

    A. 210
    B. 1050
    C. 25200
    D. 21400
    D. None of these

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    Jim@StratusPrep MBA Admissions Consultant
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    Post Mon Sep 08, 2014 4:57 am
    This is 7 choose 3 multiplied by 4 choose 2.

    n!/(n-k)!k!

    7 choose 3 = 7!/4!3! = 35

    4 choose 2 = 4!/2!2! = 6

    35 x 6 = 210

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    Post Mon Sep 08, 2014 5:22 am
    nahid078 wrote:
    Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

    A. 210
    B. 1050
    C. 25200
    D. 21400
    E. None of these
    Take the task of creating 5-letter words and break it into stages.

    Stage 1: Select the 3 consonants to work with
    Since the order in which we select the consonants does not matter, we can use combinations.
    We can select 3 consonants from 7 consonants in 7C3 ways (= 35 ways)

    Stage 2: Select the 2 vowels to work with
    Since the order in which we select the vowels does not matter, we can use combinations.
    We can select 2 vowels from 4 vowels in 4C2 ways (= 6 ways)

    If anyone is interested, we have a free video on calculating combinations (like 4C2) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789

    Stage 3: Take the 5 selected letters and arrange them.
    We can complete this stage in 5! ways (= 120 ways).

    By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25200 ways)

    Answer: C
    --------------------------

    Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775

    Then you can try solving the following questions:

    EASY
    - http://www.beatthegmat.com/what-should-be-the-answer-t267256.html
    - http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
    - http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
    - http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
    - http://www.beatthegmat.com/simple-one-t270061.html
    - http://www.beatthegmat.com/mouse-pellets-t274303.html


    MEDIUM
    - http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
    - http://www.beatthegmat.com/arabian-horses-good-one-t150703.html
    - http://www.beatthegmat.com/sub-sets-probability-t273337.html
    - http://www.beatthegmat.com/combinatorics-problem-t273180.html
    - http://www.beatthegmat.com/digits-numbers-t270127.html
    - http://www.beatthegmat.com/doubt-on-separator-method-t271047.html
    - http://www.beatthegmat.com/combinatorics-problem-t267079.html


    DIFFICULT
    - http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
    - http://www.beatthegmat.com/ps-counting-t273659.html
    - http://www.beatthegmat.com/permutation-and-combination-t273915.html
    - http://www.beatthegmat.com/please-solve-this-real-gmat-quant-question-t271499.html
    - http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html
    - http://www.beatthegmat.com/laniera-s-construction-company-is-offering-home-buyers-a-wi-t215764.html

    Cheers,
    Brent

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    Jim@StratusPrep MBA Admissions Consultant
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    Post Mon Sep 08, 2014 5:59 am
    Oops, was a bit sleepy this morning. Thanks to Brent for the next step.

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    osama_salah Just gettin' started! Default Avatar
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    Post Mon Jul 04, 2016 7:56 am
    Why did we assume that a letter can not be repeated?
    e.g. out of B,C,D,F,G,H,J and A,E,I,O we can get:
    BACAD and ECCEF

    Brent@GMATPrepNow wrote:
    nahid078 wrote:
    Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

    A. 210
    B. 1050
    C. 25200
    D. 21400
    E. None of these
    Take the task of creating 5-letter words and break it into stages.

    Stage 1: Select the 3 consonants to work with
    Since the order in which we select the consonants does not matter, we can use combinations.
    We can select 3 consonants from 7 consonants in 7C3 ways (= 35 ways)

    Stage 2: Select the 2 vowels to work with
    Since the order in which we select the vowels does not matter, we can use combinations.
    We can select 2 vowels from 4 vowels in 4C2 ways (= 6 ways)

    If anyone is interested, we have a free video on calculating combinations (like 4C2) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789

    Stage 3: Take the 5 selected letters and arrange them.
    We can complete this stage in 5! ways (= 120 ways).

    By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create all 5-letter words) in (35)(6)(120) ways (= 25200 ways)

    Answer: C
    --------------------------

    Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775

    Then you can try solving the following questions:

    EASY
    - http://www.beatthegmat.com/what-should-be-the-answer-t267256.html
    - http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
    - http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
    - http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
    - http://www.beatthegmat.com/simple-one-t270061.html
    - http://www.beatthegmat.com/mouse-pellets-t274303.html


    MEDIUM
    - http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
    - http://www.beatthegmat.com/arabian-horses-good-one-t150703.html
    - http://www.beatthegmat.com/sub-sets-probability-t273337.html
    - http://www.beatthegmat.com/combinatorics-problem-t273180.html
    - http://www.beatthegmat.com/digits-numbers-t270127.html
    - http://www.beatthegmat.com/doubt-on-separator-method-t271047.html
    - http://www.beatthegmat.com/combinatorics-problem-t267079.html


    DIFFICULT
    - http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
    - http://www.beatthegmat.com/ps-counting-t273659.html
    - http://www.beatthegmat.com/permutation-and-combination-t273915.html
    - http://www.beatthegmat.com/please-solve-this-real-gmat-quant-question-t271499.html
    - http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html
    - http://www.beatthegmat.com/laniera-s-construction-company-is-offering-home-buyers-a-wi-t215764.html

    Cheers,
    Brent

    Post Mon Jul 04, 2016 9:17 am
    osama_salah wrote:
    Why did we assume that a letter can not be repeated?
    e.g. out of B,C,D,F,G,H,J and A,E,I,O we can get:
    BACAD and ECCEF
    Good point. The question could be written to be less ambiguous.
    In fact, we don't even know that the original 7 consonants and 4 vowels are all different.
    The 11 letters could just be B,B,B,B,B,B,B,A,A,A,A

    Cheers,
    Brent

    _________________
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    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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    Matt@VeritasPrep GMAT Instructor
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    Post Thu Jul 07, 2016 3:50 pm
    osama_salah wrote:
    Why did we assume that a letter can not be repeated?
    Great question: I suppose because the answer we'd get if we DIDN'T make that assumption isn't one of the options.

    That said, (E) would fit, so it's a poorly written Q. I'm guessing it's from the CAT (a rival to the GMAT), on which I've seen other poorly written Qs, but I can't say for sure.

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