13.3 The Fundamental Counting Principle Solution Key
Jerry has 4 T-shirts, 2 pairs of jeans, and 3 pairs of shoes that can be worn together in any
combination.
1. How many ways are there for Jerry to choose an outfit?
2
3
 4 ×
×
=4×2×3=24 possibilities
shirts
pairs of jeans
pairs of shoes
Advanced Math Topics
p. 1
Wednesday, December 5, 2007
2. How many outfits can include a blue t-shirt?
2
3
 1 ×
×
=1×2×3=6 possibilities
shirt
pairs of jeans
pairs of shoes
Advanced Math Topics
p. 2
Wednesday, December 5, 2007
3. How many outfits can include a pair of black jeans?
1
3
 4 ×
×
=4×1×3=12 possibilities
shirts
pair of jeans
pairs of shoes
Advanced Math Topics
p. 3
Wednesday, December 5, 2007
4. How many outfits can include a pair of brown shoes?
2
1
 4 ×
×
=4×2×1=8 possibilities
shirts
pairs of jeans
pair of shoes
Advanced Math Topics
p. 4
Wednesday, December 5, 2007
How many ways are there to arrange the letters in each of the following words?
5. “cat”

3
2
1
×
×
=3×2×1=6 ways
first letter
second letter
third letter
6. “math”

4
3
2
1
×
×
×
=4×3×2×1=24 ways
first letter
second letter
third letter
fourth letter
7. “sport”
5×4×3×2×1=120 ways
8. “problem”
7×6×5×4×3×2×1=5,040 ways
Advanced Math Topics
p. 5
Wednesday, December 5, 2007
9. The Camachos are decorating their kitchen. There are 7 different wallpaper patterns from
which to choose. There are 5 borders that coordinate with each wallpaper pattern. How many
combinations are possible?

7
5
×
=7×5=35 combinations
wallpaper patterns
border patterns
10. Members of pep club are selling carnations. They are selling red, pink, or white carnations in
packages of 2, 4, or 6. If all carnations in a package must be the same color, how many choices
are offered?

3 ×
3
=3×3=9 choices
colors
package choices
11. A popular car model comes in 5 different colors, with a standard or automatic transmission, and
with or without a sports package. How many different types of cars are available in this model?
2
2
 5 ×
×
=5×2×2=20 types
colors
transmission choices
sports package yes/no
12. How many ways are there to name the given line?

3
2
1
×
×
=3×2×1=6 ways
first letter
second letter
third letter
13. Name all of these ways.
{
suur suur suur suur suur suur
AB, AC , BA, BC , CA, CB
Advanced Math Topics
}
p. 6
Wednesday, December 5, 2007