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\headers{Math378}{Quiz 9}{Wed. Apr. 1, 2026}
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\noindent
\hfill Name: \underline{\hspace{3.5in}} 

\noindent
\textbf{Directions:} Show all work.  You may leave your answer in terms of factorials, falling factorials, and binomial coefficients.  Any sums or products should be as simple as possible.

\begin{enumerate}

\item\ppoints{5}{2} A fair $6$-sided die is rolled $3$ times.
\begin{enumerate}
	\item Give the sample space $\Sigma$.
	\vspace{2cm}
	
	\item What is the probability that all $3$ rolls give the same value?
	\vfill
	
	\item What is the probability that all $3$ rolls give distinct values?
	\vfill
	
	\item What is the probability that among the $3$ rolls, one of the values is distinct and the other two are equal?
	\vfill
	
	\item What is the probability that at least $1$ of the rolls is a $4$?
	\vfill
\end{enumerate}

\end{enumerate}
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