The choose operator (nCr)

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Learn it $\binom{n}{r}$ ("n choose r") counts the ways to pick r things from n when order does NOT matter: $\binom{n}{r} = \frac{n!}{r!(n - r)!}$. Also $\binom{n}{r} = \binom{n}{n - r}$.

Example: How many ways can 3 students be chosen from 8?

$\binom{8}{3} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1}$
$= \frac{336}{6}$
$= 56$ ways.

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