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\begin{center}\large 
MATH 636, Fall 2014

{\sc Homework 1}

due 5:00{\sc pm} on Tuesday, September 9.
\end{center}

\noindent
{\em Background reading:} {\em Combinatorics: A Guided Tour}, Sections 1.1 and 1.2.

\smallskip\noindent
{\bf Follow the posted homework guidelines} when completing this assignment.  

\noindent
In particular, remember that you must fully justify any assertions you make.

\smallskip\noindent 
{\bf \color{red}Only} consult with your classmates or professor to discuss the problem set. 

\smallskip\noindent
Solutions to these problems should be typed (or written neatly) and handed in as class starts on Tuesday 9/9:


\begin{enumerate}
\item[\bf 1-1.] 
\begin{enumerate}
\item[(ab)] 1.1.2ab (This means parts a and b in Problem 2 of Section 1.1) 
\item[(c)] And: Assuming that the coin is fair, what is the probability that a sequence of 20 flips has exactly 10 heads and 10 tails (in any order)?
\end{enumerate}
\item[\bf 1-2.]
How many orderings are there for a deck of 52 cards if all the cards of the same suit are together?
\item[\bf 1-3.]  
\begin{enumerate}
\item 1.1.5 
\item Consider all ways to choose fifteen coins and the amount of money each way represents.  (For example, 15 dimes equals \$1.50.)  What is the smallest amount of money that occurs in at least two different ways? 
\end{enumerate}
\item[\bf 1-4.] 
\begin{enumerate}
\item How many subsets of $[30]$ contain no prime numbers?
\item How many subsets of $[30]$ have size $15$ and no numbers larger than 20?
\item How many multisubsets of $[30]$ of size $13$ have smallest element $6$ and largest element $17$?
\end{enumerate}
\item[\bf 1-5.] 1.2.9

\end{enumerate}



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