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Basket ball players

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j_shreyans GMAT Destroyer! Default Avatar
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Basket ball players Post Sat Aug 30, 2014 8:52 pm
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  • 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

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    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,
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    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

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    Cheers,
    Brent

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    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

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