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Counting PrinciplesCounting Principles Counting PrinciplesCounting Principles
Chapter 6.7Chapter 6.7
Buying a car• You can choose a Ford, Subaru, or
Porsche• You can choose a small or
medium car• You can choose red (R), purple
(P), white(W) or green (G)• How many choices do you have?
Objectives• Use the Fundamental Counting Principle
to find the number of ways 2 or more events can occur
• Find the number of ways a group of objects can be arranged in order
• Find the number of ways to choose several objects from a group without regard to order
• Use counting principles to find probabilities
The Fundamental Counting Principal
• If you have 2 events: 1 event can occur m ways and another event can occur n ways, then the number of ways that both can occur is m*n
• Event 1 = 4 types of meats• Event 2 = 3 types of bread• How many diff types of sandwiches can
you make?
• 4*3 = 12
3 or more events:• 3 events can occur m, n, & p ways, then
the number of ways all three can occur is m*n*p
• 4 meats• 3 cheeses• 3 breads• How many different sandwiches can you
make?• 4*3*3 = 36 sandwiches
The Fundamental Counting Principle
• If 1 event can occur in m ways and a second event can occur in n ways, the number of ways the 2 events can occur in sequence is m*n.
• This rule can be extended for any number of events occurring in sequence.
Buying a car• You can choose a Ford, Subaru, or
Porsche• You can choose a small or medium
car• You can choose red (R), purple (P),
white(W) or green (G)• How many choices do you have?• 3*2*3 = 18 choices
You can draw a tree diagram to show this
Tree Diagram• A tool for helping you organize the
number of possible outcomes
What is the probability of drawing a red ball and a blue ball from a sack
with a red, blue, and white ball.
Security Systems• The access code for a car’s security
system consists of 2 digits. Each digit can be 0 through 9.
• How many access codes are possible if each digit can be used only once and not repeated?
• 10*10• = 100
Security Systems• What is the probability that you
guess it on the first try?
Security Systems• The access code for a car’s security
system consists of 4 digits. Each digit can be 0 through 9.
• How many access codes are possible if each digit can be repeated?
• 10*10*10*10• = 10,000
License Plates• How many license plates can you
make if a license plate consists of• Six (out of 26) letters each of
which can be repeated?• Six (out of 26) letters each of
which can not be repeated?
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