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\usepackage{epsfig}
\newcommand{\ds}{\displaystyle}
\begin{document}
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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?

\vspace{.25in}

{\bf Answer}
\bigskip

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  &amp; = &amp; x_3 \\ A \cap O &amp; = &amp; 4
\\ A \cap B &amp; = &amp; 3 \\ B \cap O &amp; = &amp; 5 \\ O &amp; = &amp; 11 \\ A &amp; = &amp;
10 \\ B &amp; = &amp; 9 \\ 18 + x_3 &amp; = &amp; 20 \\ {\rm Hence \ \ \ } x_3 &amp; =
&amp; 2 \end{array}$
\end{center}

Hence only two children eat all three fruit.



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