The expression K! \cdot (N-K)! is a mathematical formula used in combinatorics, particularly in calculating combinations. Here, K! represents the factorial of K , which is the product of all positive integers up to K . Similarly, (N-K)! is the factorial of N-K . This formula helps in determining the number of ways to choose K items from a total of N items without regard to the order of selection. Factorials are essential in various fields, including statistics, probability, and computer science. The combination formula, often denoted as \binomNK , can be expressed using K! \cdot (N-K)! as part of its calculation. Understanding this concept is crucial for solving problems related to permutations and combinations in mathematics.