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When dealing with the occurrence of more than one event or activity, it is important to be able to quickly determine how many
possible outcomes exist.
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For example, if ice cream sundaes
come in 5 flavors with 4 possible toppings, how many different
sundaes can be made with one flavor of ice cream and one
topping? |
Rather than list the entire sample space
with all possible combinations of ice cream and toppings, we may simply
multiply: 5 • 4 = 20 possible sundaes. This simple
multiplication process is known as the
Counting
Principle.
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The Fundamental Counting
Principle: If there are
a ways for
one activity to occur, and b
ways for a second activity to occur, then there are
a • b ways for both to
occur. |
Examples:
1. Activities: roll a die and flip
a coin
There are 6 ways to roll a die and 2 ways to flip
a coin.
There are 6 • 2 = 12 ways to roll a die and flip
a coin.
2.
Activities: draw two cards from a standard deck of 52 cards without
replacing the cards
There are 52 ways to draw the first card.
There are 51 ways to draw the second card.
There are 52 • 51 = 2,652 ways to draw the two
cards.
The Counting Principle
also works for more than two activities.
3. Activities:
a coin is tossed five times
There are 2 ways to flip each coin.
There are 2 • 2 • 2 • 2 •2 = 32
arrangements of heads and tails.
4. Activities:
a die is rolled four times
There are 6 ways to roll each die.
There are 6 • 6 • 6 • 6 = 1,296 possible
outcomes.
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Remember:
The Counting Principle is easy! Simply MULTIPLY the
number of ways each activity can occur. |
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