Definition and properties of factorials

The notation called factorial notation is used in probability. Factorial notation uses the exclamation mark or point and it involves multiplication. For instance,

               4! = 4 • 3 • 2 • 1 = 24

               3! = 3 • 2 • 1 = 6

               2! = 2 • 1 = 2

               1! = 1

In general, a factorial is evaluated as follows:

n! = n (n – 1) (n – 2) • • • 3 • 2 • 1      NB: the factorial is the product of n factors, with the number decrease by 1 for each factor.

Properties:

1.      One property of factorial notation is that it can be stopped at any point by using the exclamation point or mark. For example,

 7! = 7 • 6!                    Since 6! = 6 • 5 • 4 • 3 • 2 • 1

                = 7 • 6 • 5!               Since 5! = 5 • 4 • 3 • 2 • 1

                = 7 • 6 • 5 • 4!          Since 4! = 4 • 3 • 2 • 1

                                                •

                                                •

•

               = 7 • 6 • 5 • 4 • 3 • 2 • 1

Thus, n! = n (n - 1)!

              = n (n - 1) (n - 2)!

              = n (n - 1) (n - 2) (n - 3)!       etc.

2.      Another property of factorials is 0! = 1, this fact is needed for formulas.


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