Graduate Management Admission Test (GMAT) Practice Test

What is the value of 0 factorial (0!)?

1. 0

2. 1

3. Undefined

4. 1.5

The correct answer is: 1

The value of 0 factorial (0!) is defined as 1. This definition might seem counterintuitive at first, but it can be understood from several perspectives, including combinatorics and the properties of factorials. In combinatorics, the factorial function represents the number of ways to arrange a set of items. For any number n, n! (n factorial) is the product of all positive integers up to n. When n is 0, we are essentially considering the arrangements of zero items, which can only be done in one way: by doing nothing. Thus, there is exactly one way to arrange zero items, leading us to conclude that 0! equals 1. Moreover, the factorial function can be defined recursively. According to the recursive relationship: n! = n * (n - 1)!, when n = 1, it simplifies to 1! = 1 * 0!. To maintain consistency in this formula, we observe that if 1! is equal to 1, then we must have 0! equal to 1 for the equation to hold true. This foundational concept is important in mathematics and appears frequently in areas involving permutations, combinations, and probability. Hence, acknowledging