For any whole number, the product of all the counting numbers up to and including itself. It is indicated with an exclamation point: 4! (read four factorial) is 1 2 3 4 = 24. In order for certain formulas involving permutations and combinations to work, 0! is defined to be 1. Factorials are particularly useful in calculating the number of ways an event can occur, for example, the number of possible orders of finish in a race.