Answer
$\binom{n}{r} = \frac{n!}{r!(n - r)!}$.
Explanation
In contrast, permutations $_nP_r = \frac{n!}{(n - r)!}$ account for ordering. A key property is symmetry: $\binom{n}{r} = \binom{n}{n - r}$.
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What is the formula for the number of combinations $\binom{n}{r}$ (or $_nC_r$) of choosing $r$ items from $n$ distinct objects without regard to order?
Study flashcard from the deck CSAT (Suneung) essentials: original practice.