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\def\header{{\hfill Exam 1 \hfill A. Miller \hfill Fall 2004
                                       \hfill Math 210\hfill}}
\markboth\header\header
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       \string\qquad \string\\ \string\hline}}

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%%% \outer\def\answer{ {\par\bigskip Circle your answer.} \par\medbreak

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\begin{document}

\bigskip

Show all work.  

Simplify your answers.  

Circle your answer.

\bigskip

No notes, no books, no calculator, no cell phones, no pagers, no
electronic devices. 


\par\vskip .25in
\begin{center}
Name\makebox[3in]{\hrulefill} \\
\end{center}

\bigskip
Circle your Discussion Section:
\begin{verbatim}
     DIS 343 12:05p T B329 VAN VLECK 
     DIS 344 12:05p R B321 VAN VLECK 
     DIS 345  1:20p T  595 VAN HISE  
     DIS 346  1:20p R 3401 STERLING  
\end{verbatim}
\bigskip

\begin{center} \Large
 \begin{tabular}{||c|c|c||} \hline\hline
  Problem & Points & Score \\  \hline\hline
   \input{exam.tbl}
  \hline \hline
 \end{tabular}
\end{center}

\immediate\openout\examTBLFile=exam.tbl

\bigskip
 
Solutions will be posted shortly after the exam:
www.math.wisc.edu/$\sim$miller/m210

\setcounter{page}{0}

\newpage 

\prob{6} % 1.1 - 23
Let $U=\{1,2,3,4,5,6\}$ be a universal set with subsets $X$, $Y$ and $Z$.
Suppose that 
\par $X\cup Y=\{2,4,6\}$, 
\par $X\cap Y=\{2\}$,
\par $Y^\prime\cap Z^\prime=\{1,3\}$, and
\par $Z^\prime=\{1,3,4\}$.
\par\noindent Find sets $X$, $Y$, and $Z$ which satisfy these conditions.

\answer $X=\{2,6\}$, $Y=\{2,4\}$, and $Z=\{2,5,6\}$.


\prob{6} % 1.3 - 23
An accounting firm has partners who are specialists in specific areas.
The areas of specialization and the number of partners with each
specialty are shown below.  If every partner is a specialist in a least
one area, how many partners are there?

\bigskip
\begin{tabular}{|l|l|} \hline
Specialization & Number \\ 
\hline\hline
auditing & 11 \\
consulting & 8 \\
tax & 10 \\
auditing and consulting & 3 \\
auditing and tax & 2 \\
consulting and tax & 2 \\
all three & 1 \\
\hline
\end{tabular}

\answer 23

\prob{6} % 1.4 - 23
Dorothy is considering the purchase of a new Jupiter 2005 car model
93-c. The car comes in one
of 7 colors: red, orange, yellow, green, blue, indigo, and violet. 
There are 3 optional features available: automatic transmission, sun
roof, and premium sound system.  She can purchase none of the
features, all of the features, or any set of features in between.  How many
alternatives are there for her to consider?

\answer 56

\prob{6} % 2.1 - 23
In a finite math class 10 percent withdraw, 15 percent receive
an A, 5 percent receive an AB, 20 percent receive a B, 5 percent
receive a BC, 30 percent receive a C, 10 percent receive a D, and
5 percent get an F.  

(a) What is the probability that a randomly chosen student got a grade of B or
better?  

(b) What is the probability that a randomly chosen student passed the
course(i.e. did not withdraw and got a D or better)?

\answer (a) $.40\;\;\;$ (b) $.85$


\prob{6} % 2.2 - 23
The kingdom of Mathemagic has 7 aristocrats from which three royal officers
are to be selected.  The offices are the Illustrious Incompetent, 
the Grand Pooh-Bah, and the Floundering Fool.  
One of the aristocrats is Count Jocko. 
Each aristocrat can fill at most one office.

(a) In how many ways can the offices be filled?

(b) In how many ways, if Count Jocko must be one of the officers?

(c) In how many ways, so that Count Jocko is not the Grand Pooh-Bah?

\bigskip\noindent (In part (c) Count Jocko may or may not be one of
the other officers.)

\answer (a) $210\;\;\;$ (b) $90\;\;\;$ (c) $180$

\prob{6} % 2.3 - 23
A neighborhood club has 3 girls and 6 boys.  A volleyball team of
4 players is to be selected. 

(a) How many different teams can be chosen?

(b) How many such teams have at least one boy and one girl on them?

\answer (a) $126\;\;\;$ (b) $111$

\prob{6} % 2.4 - 23
A congressional committee contain 6 democrats and 7 republicans.  One of
democrats is named Max and one of the republicans is named Max.  A
subcommittee of 5 consisting of 2 democrats and 3 republicans
is randomly selected. 
What is the probability that at least
one of the Max's is chosen?

\answer $13\over 21$


\finishtbl
\printanswers
\end{document}


