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Math Help - Determing cardinalities/options

  1. #1
    Senior Member Pinkk's Avatar
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    Determing cardinalities/options

    I have a problem that I have absolutely no idea how to approach.

    At a high school science fair, 34 students received awards for projects, 14 awards for biology projects, 13 for chemistry projects, 21 for physics projects, and 3 students got awards in all three subjects. How many students received awards for exactly one subject matter?

    Any help would be appreciated, thanks.
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  2. #2
    MHF Contributor

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    Use a Venn diagram.
    There are 3 in the intersection of all three circles.
    Work your way from inside out.
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