The notation "C(n, k)" represents the number of combinations of choosing k items from a total of n items, where the order of selection does not matter. It is calculated using the formula C(n, k) = n! / (k! * (n - k)!), where "!" denotes factorial, meaning the product of all positive integers up to that number. For example, if you have 5 fruits and want to choose 2, C(5, 2) would give you the number of ways to select those fruits. This concept is widely used in fields like statistics, probability, and combinatorics to analyze different selection scenarios.