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Math Help - A counting problem

  1. #1
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    A counting problem

    A staff member of a local university reported the following: “Out of one senior class of 500 students, 281 are taking English, 196 are taking English and History, 87 are taking History and a foreign language, 143 are taking foreign language and English, and 36 are taking all three.” Later in the week she was fired. Explain why.
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  2. #2
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    Hello, Harry!

    A staff member of a local university reported the following:

    "Out of one senior class of 500 students:
    . . 281 are taking English,
    . . 196 are taking English and History,
    . . 87 are taking History and a Language,
    . . 143 are taking English and a Language,
    . . and 36 are taking all three.”

    Later in the week she was fired. .Explain why.

    We are told that: .n(E ∩ H) = 196 .and .n(E ∩ H ∩ L) = 36
    . . Hence: .n(E ∩ H only) .= .196 - 36 .= .160

    We are told that: .n(E ∩ L) = 143 .and .n(E ∩ H ∩ L) = 36
    . . Hence: .n(E ∩ L only) .= .143 - 36 .= .107


    There are three types of English students:

    . . Those also taking History (only): . . . .160
    . . Those also taking a Language (only): .107
    . . Those taking all three courses: . . . . . .36

    Hence, there are: .160 + 107 + 36 .= .303 students taking English.

    But she reported that there are 281 students taking English.


    Fired for a simple arithmetic error?
    . . Well, maybe she did this every time.
    She might re-evaluate her career goals
    . . and learn to say, "Paper or plastic?"

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