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{\bf Question}

\bigskip
A group of 20 fussy children at a nursery are unwilling to eat the
fruit put in front of them.. The exasperated nursery assistant
observes that 10 children will eat apples, 11 will eat oranges, 9
will eat bananas, 4 will eat apples and oranges, 3 eat apples and
bananas, and 5 will eat oranges and bananas.  Draw a Venn diagram
showing fruit acceptance.  How many of the unpleasant small people
will eat all three fruit?

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{\bf Answer}
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Hidden assumption that all children will eat at least one fruit.

\begin{center}
$ \begin{array}{l}
\epsfig{file=175-10-2.eps, width=70mm}
\end{array}
\ \ \
\begin{array}{rcl} A \cap B \cap O  & = & x_3 \\ A \cap O & = & 4
\\ A \cap B & = & 3 \\ B \cap O & = & 5 \\ O & = & 11 \\ A & = &
10 \\ B & = & 9 \\ 18 + x_3 & = & 20 \\ {\rm Hence \ \ \ } x_3 & =
& 2 \end{array}$
\end{center}

Hence only two children eat all three fruit.



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