The expression k!(n-k)! is a mathematical notation used in combinatorics, specifically in calculating combinations. Here, k! (read as "k factorial") represents the product of all positive integers up to k , while (n-k)! represents the product of all positive integers up to n-k . This expression is often found in the formula for combinations, which determines how many ways you can choose k items from a total of n items. In the context of combinations, the full formula is given by \fracn!k!(n-k)! , where n! is the factorial of n . This formula helps in solving problems related to selecting groups or subsets from a larger set, such as choosing members for a team or selecting lottery numbers. Understanding k!(n-k)! is essential for grasping how these selections are calculated.