27
COUNTING RULES
As we begin our study of probability, we will often need to know the number of elements in our
sample space.
The following counting rules can help determine sample space size without
needing to list all elements.
•
Multiplication rule
If an operation can be performed in
1
n
ways, and for each of these ways, a second
operation can be performed in
2
n
ways, then the two operations together can be
performed in
2
1
n
n
ways.
Example:
How many different outcomes are there when rolling 2 dice?
•
Generalized multiplication rule
If an operation can be performed in
1
n
ways, and for each of these a second operation can
be performed in
2
n
ways, and for each of these a third operation can be performed
3
n
ways, … , and for each of these a
k
th operation can be performed
k
n
ways, then together
the
k
operations can be performed
k
n
n
n
L
2
1
ways.
Example:
A pizzeria offers the following choices for singletopping pizzas.
Sizes: 10”, 14”, 18”
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 Spring '08
 Noe
 Statistics, Counting, Probability, ways, generalized multiplication rule

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