The factorial of a positive integer is the product of all the positive integers less than or equal to it. The factorial of n is usually denoted n! The first few are 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, and 6!=720. We also define 0! to be 1 (in mathematics, an empty product has the value one).
The number n! is the number of permutations of n items (how many ways n distinct items can be arranged in a row). The number of ways you can pick r or n identical items is the binomial coefficient n!/(r!(n-r)!).