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\title{Combinations}
\author{A. U. Thor}
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\section{Combinations}
The number of combinations of size $
\mathit{k}$ from a set
of size $
\mathit{n}$ is given by the binomial coefficient
$
\left( \begin{array}{l} 
\mathit{n}
\\ 
\mathit{k}
\end{array}\right)
= 
\mathit{n}
!\linebreak [0]\ div\linebreak [0]\ 
\mathit{k}
!\linebreak [0]\ div\linebreak [0]\ 
(
\mathit{n}
- 
\mathit{k}
)
!$. A recursive definition
of $
\left( \begin{array}{l} 
\mathit{n}
\\ 
\mathit{k}
\end{array}\right)$ may be stated thus:
\[
[ 
\left( \begin{array}{l} 
\mathit{n}
\\ 
\mathit{k}
\end{array}\right)
\mathrel{\dot{=}} 
{\bf if} \ \linebreak [0]
\mathit{k}
= 
0
\ {\bf then} \ \linebreak [0]
1
\ {\bf else} \ \linebreak [0]
\left( \begin{array}{l} 
\mathit{n}
- 
1
\\ 
\mathit{k}
- 
1
\end{array}\right)
\cdot 
\mathit{n}\linebreak [0]\ div\linebreak [0]\ 
\mathit{k}
]\]
As an example, we have $
[ 
\left( \begin{array}{l} 
4
\\ 
2
\end{array}\right)
= 
6
]^{\cdot}$.
For details on how the binomial coefficient is rendered, see
\cite{appendix}.
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