Baroness Martine de Beausoleil was a French scientist in the 17th century who spent 30 years studying geology and mathematics. She determined which rocks were valuable by the minerals they contained. Some other ways to classify rocks are by their texture and by their color.
How many different rocks are possible having the
characteristics shown in the table? We can represent this situation by using a tree diagram.
By using the tree diagram, we find that there are 16
different rocks possible. These results are called outcomes. For example, the first outcome is
a rock that contains gold, has a glassy texture, and is brown. The list of all
the possible outcomes is called the sample space.
Example
Dance Link
1. The Greenwood Dance Company has three lead female dancers, Teresa,
Kendra, and Angelica, and two lead male dancers, Keith and Jamal. How many
different ways can the director choose one female dancer and one male dancer to
lead the next production?
Alternative Solutions :
Make a
tree diagram to find the number of combinations.
The sample
space contains six outcomes. So, there are six different ways that the director
can choose the leads for the next production.
An event
is a subset of the possible outcomes, or sample space. In Example 1, the
choice of female dancers is one event, and the choice of male dancers is
another event. Notice that the product of the number of choices in each event
is 3 ⋅ 2 or 6. This method of finding the number of possible
outcomes is called the Fundamental
Counting Principle.
Example
Clothing Link
2. How many different kinds of school sweatshirts are possible?
Alternative Solutions :
There are 3
styles, 2 colors, and 5 sizes, so the number of different sweatshirts is 3 × 2 × 5 or 30.
Sumber
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