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22 August, 06:46

53 freshman were interviewed about the classes they were taking this semester 24 said they were taking science 22 said they were taking math 17 said they were taking English 7 said they were taking both science and math 10 said they were taking both math and English 4 said they were taking both math and English 2 said they were taking all three classes

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  1. 22 August, 06:53
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    The questions are:

    How many students are not taking any science, math, or English? AND

    How many students are taking exactly one of science, math, or English classes?

    This is best answered using a Venn diagram. If you look at the separate areas, you see there are 7 areas.

    The common area is the two students who takes the three classes.

    4 said they were taking both math and English

    4 - 2 = 2 only take math & English

    7 said they were taking both science and math

    7 - 2 = 5 only take math and science

    10 said they were taking both science and English

    10 - 2 = 8 only take science and English

    17 said they were taking English

    17 - (2 + 8 + 2) = 5 take only English

    22 said they were taking math

    22 - (2 + 5 + 2) = 13 take math

    24 said they were taking science

    24 - (2 + 8 + 5) = 9 only take science

    Adding them all up:

    2 + 9 + 13 + 5 + 8 + 5 + 2 = 44

    So, 44 students are taking the 3 courses

    53 - 44 = 9 students are not taking any of the 3 courses

    5 + 13 + 9 = 27 take only 1 of these courses
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