The factorial of the number 0 is defined as 1 because there is only one possible permutation for a set of zero elements, namely the empty set. The combinatorial interpretation of the factorial function is the total number of possible permutations of a set of n elements.

A permutation can also be defined, in this case, as a way of arranging the objects in question. The factorial function "n!" of a positive integer n is defined as the product of all the positive integers smaller than or equal to n. It can be recursively defined as "n! = n × (n ? 1)!," where 0! and 1! are known to have the value of 1.