In mathematics, the notation "0!" represents the factorial of zero. The factorial of a number is the product of all positive integers up to that number. For example, 5! equals 5 × 4 × 3 × 2 × 1, which is 120. However, when it comes to zero, there are no positive integers to multiply, leading to the definition that 0! equals 1. This definition is useful in various mathematical contexts, particularly in combinatorics. For instance, when calculating combinations, the formula involves factorials, and having 0! equal to 1 ensures that the number of ways to choose zero items from a set is correctly represented as one way—by choosing nothing.