Page 106 - Probability Demystified

CHAPTER 6 The Counting Rules 95

The Fundamental Counting Rule

The first rule is called the Fundamental Counting Rule.

For a sequence of n events in which the first event can occur in k 1 ways
and the second event can occur in k 2 ways and the third event can occur in
k 3 ways, and so on, the total number of ways the sequence can occur is
k k k .. . k :
n
3
2
1
EXAMPLE: In order to paint a room, a person has a choice of four colors:
white, light blue, yellow, and light green; two types of paint: oil or latex; and
three types of texture: flat, semi-glass, or satin. How many different selections
can be made?

SOLUTION:
There are four colors, two types of paint, and three textures, so the total
number of ways a paint can be selected is 4 2 3 ¼ 24 ways.

EXAMPLE: There are four blood types A, B, AB, and O. Blood can be Rh þ

or Rh . Finally, a donor can be male or female. How many different
classifications can be made?

SOLUTION:

4 2 2 ¼ 16

When determining the number of different ways a sequence of events can
occur, it is necessary to know whether or not repetitions are permitted. The
next two examples show the difference between the two situations.

EXAMPLE: The employees of a company are given a 4-digit identification
number. How many different numbers are available if repetitions are
permitted?

SOLUTION:

There are 10 digits (zero through nine), so each of the four digits can be
selected in ten different ways since repetitions are permitted. Hence the
4
total number of identification numbers is 10 10 10 10 ¼ 10 ¼ 10,000.