Factorials express a product of multiple consecutive integers starting at 1. Factorials look like an exclamation point, which is placed next to either a variable or a whole number. However, even when placed next to a variable it still indicates a whole number reached by multiplying that variable by all of the integers before that variable.

So 4! = 4 • 3 • 2 • 1 or x! = x • (x−1) • (x−2)….. • 1

The main trick with factorials is to remember that when they are divided by each other, the smaller factorial will divide out and the remainder will be the product of all remaining integers from the larger factorial.

For example, 

17!14!=

17∙16∙15∙14∙13…∙114∙13∙12…= 17 • 16 • 15. So even though the fraction is being “simplified”, it is the larger numbers that will remain rather than the smaller numbers.

Since factorials are products, the above rule is true regardless of whether the larger number is in the numerator or denominator (it just determines where the remainder goes).