Basket ball players

This topic has 1 expert reply and 2 member replies
j_shreyans GMAT Destroyer! Default Avatar
Joined
07 Aug 2014
Posted:
510 messages
Followed by:
5 members
Thanked:
3 times
Basket ball players Post Sat Aug 30, 2014 8:52 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

    A)23
    B)30
    C)42
    D)60
    E)126

    OAD

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sat Aug 30, 2014 10:28 pm
    Hi j_shreyans,

    This question does NOT ask us to put players "in order", it asks us for groups of players. That clue points to using the Combination Formula. This question has 2 types of players though (guards and forwards), so we have to use the Combination Formula twice (once for each type of player), then multiply the results.

    Guards:
    There are 6 guards and we're asked for sets of 3.

    6c3 = 6!/(3!3!) = 6(5)(4)(3)(2)(1)/3(2)(1)(3)(2)(1) = 20 different sets of 3 guards

    Forwards:
    There are 3 forwards and we're asked for groups of 2.

    3c2 = 3!/(2!1!) = 3(2)(1)/(2)(1)(1) = 3 different groups of 2 forwards

    (20)(3) = 60 possible teams

    Final Answer: D

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Post Sun Aug 31, 2014 7:01 am
    j_shreyans wrote:
    9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

    A)23
    B)30
    C)42
    D)60
    E)126
    Take the task of creating a team and break it into stages.

    Stage 1: Select 3 guards from the 6 eligible guards
    Since the order in which we select the guards does not matter, we can use combinations.
    We can select 3 guards from the 6 eligible guards in 6C3 ways (= 20 ways)
    So, we can complete stage 1 in 20 ways

    If anyone is interested, we have a free video on calculating combinations (like 6C3) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789

    Stage 2: Select 2 forwards from the 3 eligible forwards
    Since the order in which we select the forwards does not matter, we can use combinations.
    We can select 2 forwards from the 3 eligible forwards in 3C2 ways (= 3 ways)
    So, we can complete stage 2 in 3 ways

    By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create a basketball team) in (20)(3) ways (= 60 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

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    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!
    Post Tue Sep 02, 2014 9:00 pm
    j_shreyans wrote:
    9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?

    A)23
    B)30
    C)42
    D)60
    E)126

    OAD
    No. of ways to select 3 Guards out of 6 guards = 6C3 = 20
    No. of ways to select 2 forwards out of 3 forwards = 3C2 = 3

    Total possible ways = 20 x 3 = 60

    Answer: Option D

    _________________
    Prosper!!!
    Bhoopendra Singh & Sushma Jha
    "GMATinsight"
    Contact Us
    Testimonials
    To register for One-on-One FREE ONLINE DEMO Class Call/e-mail
    e-mail: info@GMATinsight.com
    Mobile: +91-9999687183 / +91-9891333772
    Get in touch for SKYPE-Based Interactive Private Tutoring
    One-On-One Classes fee - US$30 per hour &
    for FULL COURSE (38 LIVE Sessions)-US$1000

    "Please click on 'Thank' if you like my post/response."

    Classroom Centres Address:
    GMATinsight
    Dwarka, New Delhi-110075 and Shivalik New Delhi

    Best Conversation Starters

    1 hazelnut01 59 topics
    2 rsarashi 21 topics
    3 NandishSS 18 topics
    4 richachampion 16 topics
    5 GMATinsight 15 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description GMATGuruNY

    The Princeton Review Teacher

    115 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    99 posts
    3 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    91 posts
    4 image description Matt@VeritasPrep

    Veritas Prep

    80 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    67 posts
    See More Top Beat The GMAT Experts