Page 203 - Math Course 3 (Book 2)

Counting Outcomes

Let’s Begin Your Turn!

Factorial
Find the value of 7!.
Use Factorials to Solve a Problem
A. 5040
Example B. 28
C. 2520
D. 720

OUTDOORS Answer
Jill and Miranda are going to a National Park for
their vacation. Near the campground where they
are staying, there are 8 hiking trails.
How many different ways can they hike all of the Find the value of 11!.
trails if they hike each trail only once?
A. 3,628,800
B. 19,958,400
C. 39,916,800
D. 79,833,600

Answer

Use Factorials to Solve a Problem
Jack and Renee want to take a cross-country trip
over the summer to 10 different cities. They are try-
ing to decide the order in which they should travel.
Use a factorial. How many different orders can they travel to the 10

8! = 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 Definition of cities if they go to each city once?
factorial A. 3,628,800
= 40,320 Simplify. B. 1,000,000
C. 100
There are 40,320 ways in which D. 10
Answer Jill and Miranda can hike all 8
trails.
Answer

If they only have time to hike 5 of the trails, in how
many ways can they do this? Suppose they only have time to go to 8 of the
cities. How many ways can they do this?
Use the Fundamental Counting Principle to count
the sample space. A. 1,000,000,000
B. 100,000,000
s = 8 • 7 • 6 • 5 • 4 Fundamental Counting C. 80
Principle D. 1,814,400
= 6720 Simplify.

There are 6720 ways that Jill and
Answer Answer
Miranda can hike 5 of the trails.

195