Examples 1 and 2 explore how to use factorial notation.

Write each expression using factorial notation, if possible.

  1. 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
  1. –4 x –3 x –2 x –1
  1. 2 x 1
  1. 5 x 3 x 1

       

  1. 8!

  2. 2!

  3. Writing this using factorial notation is not possible. Negatives are not natural numbers; they cannot be written using factorial notation.

  4. Writing this using factorial notation is not possible because it is not a consecutive list of numbers. The numbers 4 and 2 are not in the list, so "gaps" occur in the string of numbers.

 

Write each expression in expanded form if possible; then, evaluate.

  1. 5!
  1. 3!
  1. (1/2)!
  1. (–4)!

       

  1. 5 x 4 x 3 x 2 x 1 = 120

  2. 3 x 2 x 1 = 6

  3. Writing this expression in expanded form is not possible because it is undefined. Fractions are not natural numbers; they cannot be written using factorial notation.

  4. Writing this expression in expanded form is not possible because it is undefined. Negatives are not natural numbers; they cannot be written using factorial notation.