Theorem 3.4.1. Combinations of a subset without replacement.

The number of ways to select an unordered group of r items from a set of n distinct items is
\begin{equation*} _nC_r = \frac{n!}{r!(n-r)!} \end{equation*}
This is sometimes denoted C(n,r) or \(C_r^n\) or \({n \choose r}\text{.}\)

Proof.

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