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Nijo Rising GMAT Star Default Avatar
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12 Jun 2014
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Doubt Post Sat Aug 16, 2014 12:04 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Of the 12 temporary employees in a company, 4 will be made permanent. If 5 of the 12 temporary employees are male, how many groups of temp employees can consist of 3 women and 1 man?
    1)22
    2) 35
    3) 56
    4) 70
    5) 105

    OA is 70
    Thank you very much

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    Post Sat Aug 16, 2014 2:38 am
    The problem has been transcribed incorrectly.
    It should indicate that 5 of the 12 temporary employees are WOMEN:

    Quote:
    Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?

    A. 22
    B. 35
    C. 56
    D. 70
    E. 105
    Since 5 of the 12 temporary employees are women, 7 are men.
    Number of ways to choose 1 man from 7 options = 7C1 = 7.
    Number of ways to choose 3 women from 5 options = 5C3 = (5*4*3)/(3*2*1) = 10.
    To combine the options above, we multiply:
    7*10 = 70.

    The correct answer is D.

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    Post Sat Aug 16, 2014 6:55 am
    Quote:
    Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?

    A. 22
    B. 35
    C. 56
    D. 70
    E. 105
    Take the task of selecting the employees and break it into stages.

    Stage 1: Select the 3 women
    The order in which we select the women does not matter, so we can use combinations.
    We can select 3 women from 5 women in 5C3 ways (= 10 ways)

    Aside: If anyone is interested, we have a free video on calculating combinations (like 5C3) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789

    Stage 2: Select the 1 man
    There are 7 men, so we can complete this stage in 7 ways.

    By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select the permanent employees) in (10)(7) ways (= 70 ways)

    Answer: D
    --------------------------

    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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    Thanked by: manik11
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    Gurpreet singh Rising GMAT Star Default Avatar
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    Post Sun Jun 26, 2016 5:23 pm
    Question stem says 5 of 12 emp are male, while the calculations have been done for female

    Post Sun Jun 26, 2016 5:27 pm
    Gurpreet singh wrote:
    Question stem says 5 of 12 emp are male, while the calculations have been done for female
    Check out Mitch's post (second from top.) He notes that the initial question had been transcribed incorrectly.

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    Gurpreet singh Rising GMAT Star Default Avatar
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    Post Mon Jun 27, 2016 12:24 am
    Sorry missed it.
    Thank you.

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