Probability And Statistics Worksheets Page 23
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429-5
Permutations and
Combinations
■
Goals
Find the number of permutations and combinations
of a set.
Applications
Travel, Sports, Office Work
Work with a partner to answer the questions.
You have just applied for your first set of license plates. Each license plate has 3
different letters followed by 3 different digits. The letters and digits are assigned
randomly by the Department of Motor Vehicles.
1. How many arrangements of 3 different letters are possible?
2. How many arrangements of 3 different digits are possible? Remember, to
include 0 as a digit.
3. Suppose you had hoped that your plate would read “ACE 123.” What is the
probability that you will receive this plate? How do you know?
B
U
UILD
NDERSTANDING
Thus far, you have used either a tree diagram or a set of ordered pairs to find the
number of outcomes in a sample space. But sometimes the sample space is too
large to use either of these methods.
Another way to find the total number of outcomes is to use the fundamental
counting principle. This principle can be used to calculate the number of ways two
or more events can happen in succession. It states that, if an event A can occur in
m ways and an event B can occur in n ways, then events A and B can happen in
m n ways.
E x a m p l e 1
TRAVEL
Suppose the Carthage College Women’s Basketball team will
travel on a road trip to Grand Rapids, Peoria, and Battle Creek. They
can go from Kenosha to Grand Rapids by car, train, or bus, then from
Grand Rapids to Peoria by bus, train, or plane, and from there to Battle
Creek by car, bus, train, or plane. Finally, from Battle Creek, they can
either take the bus or the train back to Kenosha. How many different
routes are possible on this road trip?
Solution
Use the fundamental counting principle.
The 3 possible routes for the first leg of the trip are car, train, or bus.
Then they have 3 possible routes for the second leg of the trip, 4 for
the third leg of the trip, and 2 for the return trip to Kenosha.
3 3 4 2
72
Seventy-two different routes are possible.
402
Chapter 9 Probability and Statistics
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