The formula C(N, K) = \fracN!K! \cdot (N-K)! is used to calculate combinations, which represent the number of ways to choose K items from a total of N items without regard to the order of selection. Here, N! (N factorial) is the product of all positive integers up to N , and similarly for K! and (N-K)! . In this context, C(N, K) is essential in fields like statistics, probability, and combinatorics. It helps in solving problems related to lottery, card games, and various scenarios where selection is involved, providing a systematic way to count possible outcomes.