Page 206 - Math Course 3 (Book 2)

Permutations and Combinations

Permutation and Probability
Your Turn!

Example Tree Diagram Permutation

There are five finalists in the student art contest:
Shaquille has a 5-digit pass code to access his Cal, Jeanette, Emily, Elizabeth, and Ron. The winner
e-mail account. The code is made up of the and the runner-up of the contest will receive prizes.
even digits 2, 4, 6, 8, and 0. Each digit can be How many possible ways are there for the winners
used only once. How many different pass codes to be chosen?
could Shaquille have?
A. 20
Since the order of the numbers in the code is B. 15
important, this situation is a permutation of 5 C. 120
digits taken 5 at a time. D. 5

n! Definition of Answer
P = permutation
n r (n – r)!
5!
P = n = 5, r = 5
5 5 (5 – 5)!

5 • 4 • 3 • 2 • 1
P = or 120 Definition of
5 5 1 factorial

There are 120 possible pass
Answer codes with the digits 2, 4, 6, 8,
and 0.

What is the probability that the first two digits of
his code are both greater than 5?
Permutation and Probability
Use the Fundamental Counting Principle to
determine the number of ways for the first two Bridget and Brittany are trying to find a house, but
digits to be greater than 5. they cannot remember the address. They can re-
member only that the digits used are 1, 2, 5, and 8,
• There are 2 digits greater than 5 and 3 digits and that no digit is used twice. How many possible
less than 5. addresses are there?

• The number of choices for the first two digits, A. 12
if they are greater than 5, is 2 • 1. B. 24
C. 16
• The number of choices for the remaining digits D. 9
is 3 • 2 • 1.
Answer
• The number of favorable outcomes is 2 • 1 • 3
• 2 • 1 or 12. There are 12 ways for this event What is the probability that the first two digits are
to occur out of the 120 possible permutations. odd?

12 ←number of favorable outcomes
P(first 2 digits > 5) = 1
20 ←number of possible outcomes A. 2
1 1
= Simplify B. 3
10 1
C. 4
The probability that the first two 1
Answer digits of the pass code are greater D. 6
1
than 5 is or 10%.
10 Answer
198