Exercise 1.4

Question

A round-robin tournament is being held with n tennis players; this means that every player will play against every other player exactly once.
\begin{enumerate}[label=(\alph*)]
\item How many possible outcomes are there for the tournament (the outcome lists out
who won and who lost for each game)?
\item How many games are played in total?
\end{enumerate}

fifthist x · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item There are ${n \choose 2}$ matches.

For a given match, there are two outcomes. Each match has two possible outcomes. 
We can use the multiplication rule to count the total possible outcomes.

$$ 2^{{n \choose 2}} $$

\item Since every player plays every other player exactly once, the number of 
games are the number of ways to pair up to $n$ people.

$$ {n \choose 2} $$
\end{enumerate}

Exercise 1.4

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Exercise 1.4

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