FACTORIAL NOTATION
(and Counting Principles)
FACTORIAL NOTATION:
notation used to write the product of a
series of consecutive integers
FACTORIAL NOTATION:
n! = n(n - 1)(n - 2)(n - 3) … 3 x 2 x 1, n  N
with 0! = 1
For example, 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
=
NOTE:
In every factorial, there exists every smaller factorial.
8! =
=
=
=
EXAMPLE #1
a) 9!
EXAMPLE #2
8
8
8
8
x 7!
x 7 x 6!
x 7 x 6 x 5!
x 7 x 6 x 5 x 4!
etc.
Evaluate each of the following:
b) 15!
c) 49!
Express each of the following in factorial notation:
a) 7 x 6 x 5 x 4 x 3 x 2 x 1
b) 15 x 14 x 13 x 12!
c) (n+1)(n)(n-1)…3 x 2 x 1
d) (n+4)(n+3)(n+2)!
EXAMPLE #3
a)
Evaluate each of the following:
10!
7!
EXAMPLE #4
b)
Express in factorial notation:
a) 10 x 9 x 8 x 7
EXAMPLE #5
12!
8! 3!
b)
8x7 x6
5x 4
Determine the number of ways a group of 6
children can line up at a door if:
a) there are no restrictions;
b) the 2 tallest children must be at the end of the line;
c) Barney and Fred cannot be beside each other.