Page 108 - Probability Demystified

CHAPTER 6 The Counting Rules 97

Factorials

In mathematics there is a notation called factorial notation, which uses the
exclamation point. Some examples of factorial notation are
6! ¼ 6 5 4 3 2 1 ¼ 720
3! ¼ 3 2 1 ¼ 6
5! ¼ 5 4 3 2 1 ¼ 120
1! ¼ 1

Notice that factorial notation means to start with the number and find its
product with all of the whole numbers less than the number and stopping at
one. Formally defined,
n! ¼ n ðn 1Þ ðn 2Þ .. . 3 2 1
Factorial notation can be stopped at any time. For example,

6! ¼ 6 5! ¼ 6 5 4!
10! ¼ 10 9! ¼ 10 9 8!
In order to use the formulas in the rest of the chapter, it is necessary to
know how to multiply and divide factorials. In order to multiply factorials,
it is necessary to multiply them out and then multiply the products. For
example,
3! 4! ¼ 3 2 1 4 3 2 1 ¼ 144

Notice 3! 4! 6¼ 12! Since 12! ¼ 479,001,600

EXAMPLE: Find the product of 5! 4!

SOLUTION:
5! 4! ¼ 5 4 3 2 1 4 3 2 1 ¼ 2880

Division of factorials is somewhat tricky. You can always multiply them
out and then divide the top number by the bottom number. For example,

8! 8 7 6 5 4 3 2 1 40;320
¼ ¼ ¼ 56
6! 6 5 4 3 2 1 720