Definition
A combination is the number of unordered subsets that can be formed from a set of finite objects. Not to be confused with a permutation, which is the number of ordered subsets that can be formed from a set of finite objects.
The combination is also referred to as $n$ choose $k$, as in, out of $n$ objects, choose $k$ of them. This is denoted by
\(\binom{n}{k} = \frac{n!}{k! (n-k)!}\)
Examples
The number of possible hands in poker can be computed with a combination. There are $n = 52$ cards in a standard deck and a poker hand chooses $k = 5$ of them, so the number of distinct possible poker hands is
\[\binom{n}{k} = \binom{52}{5} = \frac{52!}{5!(52-7)!} = 2,598,960.\]Importantly, note that poker hands are the same regardless of the order you receive the cards.