Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - How do I use Combinatorics to read Venn diagrams?

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Phoenix, AZ
    Posts
    13

    How do I use Combinatorics to read Venn diagrams?

    The problem looks like this:

    Stephen asked 100 coffee drinkers whether they like cream or sugar in their coffee. According to the Venn diagram below, how many like:

    a) Cream?

    b) Sugar?

    c) Sugar but not cream?

    d) Cream but not sugar?

    e) Cream and sugar?

    f) Cream or sugar?

    g) Black (no cream, no sugar)?


    Also, the Venn Diagram picture is attached. In the "Cream" section of the Venn diagram, it states that there are 16 coffee drinkers who like cream. There are 35 for sugar, and in the overlap area there are 20.

    How do I solve these problems? Am I over-thinking it?
    Attached Thumbnails Attached Thumbnails How do I use Combinatorics to read Venn diagrams?-hw-11-discrete-venn-diagram.bmp  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780

    Re: How do I use Combinatorics to read Venn diagrams?

    Quote Originally Posted by alexthesauceboss View Post
    How do I solve these problems? Am I over-thinking it?
    Possibly. For a start, I assume you can answer c), d) and e). The answers come straight from the picture; no arithmetic is necessary.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    Phoenix, AZ
    Posts
    13

    Re: How do I use Combinatorics to read Venn diagrams?

    Quote Originally Posted by emakarov View Post
    Possibly. For a start, I assume you can answer c), d) and e). The answers come straight from the picture; no arithmetic is necessary.
    c) 55 (sugar but not cream I assume means the overlap and the sugar section added together)
    d) 36 (cream but not sugar I assume means the overlap and the cream section added together)
    e)20 (I assume cream or sugar means just the overlap)

    I'll be back in about 3 and a half hours if someone wants to continue to help me.
    Last edited by alexthesauceboss; January 29th 2013 at 01:30 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780

    Re: How do I use Combinatorics to read Venn diagrams?

    Quote Originally Posted by alexthesauceboss View Post
    c) 55 (sugar but not cream I assume means the overlap and the sugar section added together)
    This cannot be right for two reasons. First, I said that no arithmetic is necessary. Second, the overlap represents those who like both cream and sugar; in particular, they like cream. And here you are asked about those who like sugar but not cream!.

    Quote Originally Posted by alexthesauceboss View Post
    d) 36 (cream but not sugar I assume means the overlap and the cream section added together)
    Wrong for the same reasons.

    Quote Originally Posted by alexthesauceboss View Post
    e)20 (I assume cream or sugar means just the overlap)
    Correct.
    Thanks from alexthesauceboss
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2013
    From
    Phoenix, AZ
    Posts
    13

    Re: How do I use Combinatorics to read Venn diagrams?

    Quote Originally Posted by emakarov View Post
    This cannot be right for two reasons. First, I said that no arithmetic is necessary. Second, the overlap represents those who like both cream and sugar; in particular, they like cream. And here you are asked about those who like sugar but not cream!.

    Wrong for the same reasons.

    Correct.
    So then C) is 35, D) is 16, and e) is 20...Do the rest require combinatorics?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,540
    Thanks
    780

    Re: How do I use Combinatorics to read Venn diagrams?

    Quote Originally Posted by alexthesauceboss View Post
    So then C) is 35, D) is 16, and e) is 20...
    Yes.

    Quote Originally Posted by alexthesauceboss View Post
    Do the rest require combinatorics?
    Your answers in post #3 are in fact answers to b) and a). (Why?) For f), note that the three areas in the picture are disjoint, i.e., no person belongs to two groups simultaneously. This means that to find the number of people in all three groups you just need to add the numbers. Finally, that sum is going to be less than 100, and the rest like their coffee black.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Venn diagrams
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 8th 2011, 03:01 AM
  2. Venn Diagrams
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 12th 2010, 01:14 PM
  3. Venn Diagrams
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: September 25th 2008, 03:56 AM
  4. Venn Diagrams
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: June 24th 2008, 10:09 AM
  5. Venn Diagrams
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 23rd 2008, 03:29 PM

Search Tags


/mathhelpforum @mathhelpforum