## Definition A ==Combination== is a selection of $k$ objects from a set of $n$ distinct objects where the **order does not matter**. The number of combinations is given by the binomial coefficient: $ \binom{n}{k} = \frac{n!}{k!(n-k)!} $ > [!example]- A committee of 3 is to be chosen from 10 people. How many different committees are possible? > Since the order of selection doesn't matter, we use a combination: > $ \binom{10}{3} = \frac{10!}{3! \cdot 7!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 $