The factorial of a natural number n, denoted n!, is defined as the product of natural numbers from 1 to n. This is a familiar concept to students. Although this concept is defined simply, the function n! increases very rapidly, making calculations difficult. Therefore, one seeks ways to approximate n!. A well-known approximation formula currently in use is the Stirling formula (formula (1.1)). To prove the approximation of n! using this formula, in analysis, Laplace integrals, Euler-Maclaurin formulas... have been used. In this paper, we use the properties of the exponential distribution combined with some limit theorems to prove the approximation of the value n! when n is large.