Factorial

The factorial n! gives the number of ways in which n objects can be permuted. For example, 3! = 6, since the six possible permutations of {1,2,3} are {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1}. !0 is defined as 1 just as an empty set {} has one possible permutation {}.

• 0! = 1
• 1! = 1
• 2! = 1*2 = 2
• 3! = 1*2*3 = 6
• 4! = 1*2*3*4 = 24
• 5! = 1*2*3*4*5 = 120
• 20! = 1*2...19*20 = 2 432 902 008 176 640 000