Combinations Basics
Combinations count the number of ways to select items from a set where order does not matter.
Combination Formula
The number of ways to choose \(k\) items from \(n\) is:
\[ C(n, k) = \frac{n!}{k!(n-k)!} \]
Example
How many ways to choose 2 fruits from \{apple, banana, orange\}?
\[ C(3, 2) = \frac{3!}{2!(3-2)!} = \frac{6}{2 \cdot 1} = 3 \]
Selections: \{apple, banana\}, \{apple, orange\}, \{banana, orange\}.
Applications
Combinations are used in lottery odds, team selection, and statistical sampling.