Geometry
Name
10.1 Sample Space and Fundamental Counting Principle
Pd.
Determine the sample space by listing the elements of the sample space in set notation. Then, determine
the number of possible outcomes.
1. The numbers on the spinner.
2. The letters on the spinner
____________________________________
size of sample space
__________
# of possible outcomes __________
3. The factors of 16.
size of sample space
__________
# of possible outcomes __________
4. A bag of marbles with 3 Red, 2 Green and 5 Yellow
____________________________________
size of sample space
____________________________________
__________
# of possible outcomes __________
____________________________________
size of sample space
__________
# of possible outcomes __________
5. You are trying to decide what to eat for breakfast. You can choose a main course (eggs, pancakes, or
waffles), side (bacon or sausage), and drink (coffee and orange juice). Make a tree diagram to find
the sample space and find the total number of meals that can be made by choosing a main course,
side, and drink.
Sample space: (as a tree diagram)
Total number of meals_________
*****Directions: Please write down your calculations for full credit.*****
6. There are 3 options on a car at a dealership. You need to decide if you want manual or automatic
transmission. There are different trim options (EX, LX, SX) and exterior paint options (red, white,
black or silver). How many outcomes are there for these three options?
___________
7. In 2014, one type of Illinois license plate had two letters followed by four digits. How many of this
type of license plate were possible if…
a. Letters and digits can be repeated?
_________________________________
b. Letters cannot be repeated ?
_________________________________
c. Letters and digits cannot be repeated ?
_________________________________
8. There is going to be an election for officers in the newly formed Math club. There are 3 candidates for
President, 4 candidates for Vice-President, 2 candidates for Secretary, and 5 for Treasurer. In how
many ways can the offices be filled?
____________
9. Ten students are in a race. First, second, and third places will win medals. In how many ways can ten
runners finish first, second, and third (no ties allowed)?
____________
10. How many ways can you arrange 8 shirts on hangers in a closet?
_____________
11. How many ways can you file 12 folders, one after another, in a drawer?
_____________
12. You should rotate tires on a car at regular intervals.
a. In how many ways can four tires be arranged on a car?
_____________
b. If a spare tire is included, how many arrangements are possible?
_____________