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Math Help - Help with choosing subsets question

  1. #1
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    Help with choosing subsets question

    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(12,2)*C(7,2)*C(15,1)

    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:

    1) Pick 2 males out of 5 who are tall enough, 1 female who is tall enough, pick another female so we have min. amount of males and females, and 15 choices for the last team member. So: C(5,2)*C(1,1)*C(6,1)*C(15,1).

    2) Pick 3 males out of 5 who are tall enough, 2 females and 15 choices for last team member: C(5,3)*C(7,2)*C(15,1)

    Add 1) + 2) which gives us the total number of ways. Is this correct? I am unsure...it seems to give a very large number!

    Thanks for any help,

    combinatorixxx
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  2. #2
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    Re: Help with choosing subsets question

    Quote Originally Posted by combinatorixxx View Post
    [B]"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?
    Answer: \dbinom{12}{2}\dbinom{7}{3}+\dbinom{12}{3}\dbinom{  7}{2}.
    WHY?
    Thanks from combinatorixxx
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  3. #3
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    Re: Help with choosing subsets question

    Quote Originally Posted by Plato View Post
    Answer: \dbinom{12}{2}\dbinom{7}{3}+\dbinom{12}{3}\dbinom{  7}{2}.
    WHY?
    We can choose in two ways - 2 males and 3 females, or 3 males and 2 females.

    Hmm it makes sense now but I find it difficult to think in the correct way.

    So for the second part, would we have:

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

    \dbinom{5}{2}\dbinom{1}{1}\dbinom{6}{2}+\dbinom{5}  {2}\dbinom{1}{1}\dbinom{6}{1}\dbinom{10}{1} + \dbinom{5}{3}\dbinom{7}{2}
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  4. #4
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    Re: Help with choosing subsets question

    Hi friends, even I not good enough in solving such problem but I enjoy lot by seeing you guys solving such problems of math.
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