1. 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.

2. 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?"