Page 107 - Probability Demystified

96 CHAPTER 6 The Counting Rules

EXAMPLE: The employees of a company are given 4-digit identification
numbers; however, repetitions are not allowed. How many different numbers
are available?

SOLUTION:
In this case, there are 10 ways to select the first digit, 9 ways to select the
second digit, 8 ways to select the third digit, and 7 ways to select the fourth
digit, so the total number of ways is 10 9 8 7 ¼ 5040.

PRACTICE

1. A person can select eight different colors for an automobile body,
five different colors for the interior, and white or black sidewall tires.
How many different color combinations are there for the automobile?
2. A person can select one of five different colors for brick borders, one
type of six different ground coverings, and one of three different types
of shrubbery. How many different types of landscape designs are
there?
3. How many different types of identification cards consisting of 4 letters
can be made from the first five letters of the alphabet if repetitions are
allowed?
4. How many different types of identification cards consisting of 4 letters
can be made from the first 5 letters of the alphabet if repetitions are
not allowed?
5. A license plate consists of 2 letters and 3 digits. How many different
plates can be made if repetitions are permitted? How many can be
made if repetitions are not permitted?

ANSWERS

1. 8 5 2 ¼ 80 color combinations
2. 5 6 3 ¼ 90 types
4
3. 5 5 5 5 ¼ 5 ¼ 625 cards
4. 5 4 3 2 ¼ 120 cards
5. Repetitions permitted: 26 26 10 10 10 ¼ 676,000
Repetitions not permitted 26 25 10 9 8 ¼ 468,000