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COMPUTER SCIENCE 20, SPRING 2012 \\
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\\
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Class \#23 (Counting Subsets)
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\paragraph{Homework, due in hard copy Wednesday 4/4/2012 at 10:10am}
\paragraph{Please write your TF's name on your homework, and list the names of any students with whom you collaborated.}
\begin{enumerate}
\item How many length-7 bit strings have more 1s than 0s or an even number of 1s?
\item In the hopes of making millions, you head over to the poker table.\footnote{Luck be a lady tonight!}
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\item A \textit{royal flush} is a 5-card poker hand that has the Ace, King, Queen, Jack, and 10 of a single suit. How many ways are there to be dealt a royal flush, assuming the order in which the cards are received does not matter?
\item A \textit{pair} is a 5-card poker hand that has two cards of the same rank and three cards of different rank from each other and from the pair. How many ways are there to be dealt a pair?
\item What is the ratio of royal flush hands to pairs?
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