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{{\Large\bf MODERN ALGEBRA I}\\
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{\Large\bf HOMEWORK ASSIGNMENT III}\\
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{\bf (Turn in underlined problems.)}}
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{\bf 
\begin{tabbing}
\underline{\large\bf CHAPTER}\makebox[2in]{}\=\underline{\large\bf PROBLEMS}\\

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\noindent
1 \> \underline{1.43}, \underline{1.44},
\underline{1.46}
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\noindent
\underline{\large\bf ADDITIONAL PROBLEMS}
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{\bf 

\underline{1.} Show that if $p$ is prime, then 
$p$ divides
$\displaystyle 
\left(\begin{array}{c} p\\ k\end{array}\right)$
whenever $0 < k < p$.

\bigskip

\underline{2.} Show that if $n>1$ is not prime, then 
$n$ does not divide
$\displaystyle 
\left(\begin{array}{c} n\\ k\end{array}\right)$
for some $0 < k < n$.
(Hint: Choose $k$ to be a prime
divisor of $n$.)

\bigskip

3. What is the probability that a randomly chosen
binomial coefficient is even?
(You may interpret {\em probability}
and {\em random} in any reasonable way.)


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