Probability Review

1
Probability Review

• The Fundamental Counting Principle, Permutations,
  and
• Combinations

2
There are 3 roads I can choose from to get from
my driveway to any of the side streets in my
neighborhood, 2 roads I can choose from that will
take me from the side streets to any of the main
streets, and 4 main streets that will take me
from the side streets to the highway. How many
different ways can I get from my driveway to the
highway?
3
There are 3 roads I can choose from to get from
my driveway to any of the side streets in my
neighborhood, 2 roads I can choose from that will
take me from the side streets to any of the main
streets, and 4 main streets that will take me
from the side streets to the highway. How many
different ways can I get from my driveway to the
highway?3 x 2 x 4 24
4
There are 24 crayons that are all different
colors. I have to share the crayons with the 3
other people at my table, so we each get 6
crayons. How many possible combinations of colors
could I get out of the 24 crayons?
5
There are 24 crayons that are all different
colors. I have to share the crayons with the 3
other people at my table, so we each get 6
crayons. How many possible combinations of colors
could I get out of the 24 crayons?24C6
24P6/6! 24x23x22x21x20x19/6x5x4x3x2x1134,596
6
There are 15 songs on my CD and 4 dances I could
do to any of the songs. How many different ways
could I combine the dances with the songs?
7
There are 15 songs on my CD and 4 dances I could
do to any of the songs. How many different ways
could I combine the dances with the songs?15 x
4 60
8
I am creating a stained glass hanging for my
house. It will have 4 layers of colors
overlapping one another. I have the following
colors with which to work blue, green, yellow,
red, purple, orange, and pink. How many different
ways could I create the stained glass hanging? 
9
I am creating a stained glass hanging for my
house. It will have 4 layers of colors
overlapping one another. I have the following
colors with which to work blue, green, yellow,
red, purple, orange, and pink. How many different
ways could I create the stained glass
hanging?7P4 7 x 6 x 5 x 4 840 
10
No one ever sharpens there pencil until the last
minute. Yesterday, half of my class had to
sharpen their pencils right before a test. If
there are 12 students in my class, how many ways
could the kids waiting to sharpen their pencil
line up?
11
No one ever sharpens there pencil until the last
minute. Yesterday, half of my class had to
sharpen their pencils right before a test. If
there are 12 students in my class, how many ways
could the kids waiting to sharpen their pencil
line up?6P6 6! 6x5x4x3x2x1 720
12
A furniture store sells couches that are
available in 3 different styles, 7 different
colors, and 2 different sizes. How many different
couches are available?
13
A furniture store sells couches that are
available in 3 different styles, 7 different
colors, and 2 different sizes. How many different
couches are available?3 x 7 x 2 3 x 14 42
14
There are 20 students in my math class. If I have
to pick the top 3 students, how many ways can I
pick them?
15
There are 20 students in my math class. If I have
to pick the top 3 students, how many ways can I
pick them?20C3 20P3/3! 20 X 19 X 18 / 3 X 2
X 11140
16
You have 4 coins a penny, a nickel, a dime, and
a quarter. How many different amounts of money
can you form using 3 coins?
17
You have 4 coins a penny, a nickel, a dime, and
a quarter. How many different amounts of money
can you form using 3 coins?4C3 4P3/3! 4 x 3
x 2 / 3 x 2 x 1 4
18
In wrapping a gift, you have a choice of 3
different boxes, 4 different wrapping papers, and
2 different types of bows. In how many different
ways can you wrap the gift?
19
In wrapping a gift, you have a choice of 3
different boxes, 4 different wrapping papers, and
2 different types of bows. In how many different
ways can you wrap the gift?3 x 4 x 2 24
20
In how many different ways can you arrange 5
different cards taken 3 at a time?
21
In how many different ways can you arrange 5
different cards taken 3 at a time?5P3 5 x 4 x
3 60