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Choosing subsets

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    Greetings,

    I am currently struggling on this question:

    "A team has to be selected in the following way:
    - 5 players
    - at least 2 men and at least 2 women
    - there are 12 men and 7 women"

    i) How many ways can the team be selected?

    I think this is just C(12,3)*C(7,3) + C(12,3)*C(7,2)

    ii) The team must now also include 3 players of height greater than 7ft.
    5 males and 1 female have height satisfying this.
    How many ways can we pick this?

    My method so far is:

    2 tall males, 1 tall female, 2 females
    2 tall males, 1 tall female, 1 female, 1 male
    3 tall males, 2 females

    (5,2)*(1,1)*(6,2) + (5,2)*(1,1)*(6,1)*(10,1) + (5,3)*(7,2)

    Thanks for any help,

    combinatorixxx
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    You can't use binomials because you're choosing people without replacement - you need to use the hypergeometric distribution instead.
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    (Original post by mmmpie)
    You can't use binomials because you're choosing people without replacement - you need to use the hypergeometric distribution instead.
    Are you sure?

    We don't study any distributions in this course; it's a maths module not stats.

    I'm pretty sure we're meant to use binomials.
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    (Original post by combinatorix)
    Are you sure?

    We don't study any distributions in this course; it's a maths module not stats.

    I'm pretty sure we're meant to use binomials.
    No, thinking about it it's just a choose. You're right, sorry. I'm at the end of an all nighter and really shouldn't be trying to answer questions
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    I think you need to be careful about the following two cases:

    2 tall males, 1 tall female, 1 female, 1 male
    3 tall males, 2 females

    In particular, the scenario "2 tall males, 1 tall female, 1 female, 1 tall male" seems to be counted under both categories.

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Updated: May 3, 2012
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