An exclamation point in math typically represents a factorial. The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n.
For example, if we have 5!, it means:
5! = 5 × 4 × 3 × 2 × 1 = 120.
Factorials are commonly used in permutations and combinations, helping to calculate the number of ways to arrange or select items. For instance, if you wanted to determine how many different ways you can arrange three books on a shelf, you would use 3!, which equals 6 arrangements:
3! = 3 × 2 × 1 = 6.
This concept is crucial in fields such as statistics, algebra, and calculus, and it’s important to remember that 0! is defined as 1 to ensure consistency in calculations.