Data Analysis and Probability
Name
Interventions and Extensions 2 - Red
__
Date_______________
Permutation
Score
/60
Combination
• Describes a grouping of objects in which
order _______ important
• Describes a grouping of objects in which
order __________ important
• If John, Romeo, and Shelly all won prizes
at the tennis tournament, it matters who
won first prize, who won second prize, and
who won third prize.
• If John, Romeo, and Shelly are chosen to
compete in the tennis tournament, it doesn’t
matter in what order they are selected.
• The number of permutations of x items,
chosen from a total of n items
n!
n Px 
 n  x !
• Example: The number of ways that
3 objects can be selected from a total of
5 objects in a certain order.
• The number of combinations of x items,
chosen from a total of n items
n Cx

n!
x !  n  x !
• Example: The number of ways that
3 objects can be selected from a total of
5 objects in no particular order.
Evaluate the
following permutations and combinations.
1.
4C2
2.
________________________
4.
5P1
________________________
4P2
3.
________________________
5.
3P3
________________________
5C1
_________________________
6.
7C6
_________________________
Would you use a permutation or a combination to determine each of the following?
7. Nathan has a dozen eggs. He wants to decorate
4 eggs for an art project.
8. Mr. Gunther is lining up 12 kindergarten students
for a performance.
9. Rachel has 10 valuable baseball cards. She wants
to select 2 of them to sell online.
10. Don has 5 soccer trophies to line up on the mantel
of his fireplace.
11. Bree has to select 5 photos from a box containing
25 photos to use in the yearbook.
You can predict the likelihood that an event will take place by calculating the _____________ (P) of it
occurring. In order to calculate the probability of an event occurring, you need to know all the possible
____________ of an event.
The number of __________ outcomes
n
P
t
If you toss a dime,
there are ___ possible
outcomes: heads and
tails.
The number of _______ outcomes
If you roll a number
cube, there are 6
possible outcomes are:
If you draw a card
from a full deck, there
are _____ possible
outcomes.
If you randomly
choose one day of the
week, there are _____
possible outcomes.
Identify n and t in each statement.
12. There are 3 black kittens in a litter of 6 kittens.
_______________________
13. In a box of 8 donuts, 2 are chocolate.
_______________________
14. Half the children in the 16-student class are girls.
_______________________
15. Harry put a silver dollar in 4 of the 12 grab bags.
_______________________
16. Which measure will not give
the typical value of the data
set when an outlier is present?
17.In the data set {1, 1, 2, 2, 2, 3},
why is 1 not a mode?
18.When finding a median, when
will you have to take the mean of
two numbers?
19.Why does the adding an outlier to
a data set have no effect on the mode?
20.Find the mean, median, and mode of {7, 3, 10, 15, 10, 3}.
Data Analysis and Probability Interventions and Extensions 2 - Yellow
Name
__
Date_______________
Score
/60c
Rosalie is looking at locks. The label combination lock confuses her. She wonders
about the number of possible permutations or combinations a lock can have.
1.She looks at one circular lock with 12 positions. To open it she turns the dial clockwise to
a first position, then counterclockwise to a second position, then clockwise to a third position
a. Write an expression for the number of 3-position codes
that are possible, if no position is repeated.
b. Explain how this represents a combination or a permutation.
2. Rosalie looks at cable locks. Each position can be set from 0 to 9. How many different codes are possible
for each lock if no digits are repeated in each code?
a. a 3-digit cable lock
b. a 4-digit cable lock
c. a 6-digit cable lock
3. Rosalie needs 2 cable locks, but there are 13 types of locks to choose from.
a. In how many ways can she choose 2 different locks?
b. Explain how this represents a permutation or a combination.
4. Tia and her friends earned extra money by babysitting children in their neighborhood. Tia created a
table to show their earnings. Taylor noticed that Tia made a mistake, her actual earnings was $55,
not $87. How much does this mistake affect the mean of the group?
Name
Tia
Sierra
Alexis
Jayla
Ja’Shauna
Diamond
Taylor
Earnings
$52
$49
$45
$60
$52
$65
$87
The table shows the results of a spinner experiment. Use the table to find each
experimental probability.
Spinner Experiment
Number
1
2
3
4
Spins
15
10
8
22
5. Spinning a 3
a. What is the total number of trials?
b. Find the probability.
6. Spinning an even number
a.What is the number of even spins?
b. Find the probability.
7. Spinning 1 or 2
a. How many trials resulted in a 1 or a 2?
b. Find the probability.
8. The amounts due on the Harvey’s electric bill, rounded to the nearest dollar, for the past six months were
$64, $83, $76, $134, $76, and $71. Find the mean, median, and mode of the amounts. Which value should Mr.
Harvey tell his family to convince them to cut down on electric use?
9. Rachel needs to get an 85 percent overall in her college class. Her overall grade is the average of all her
test scores. Her first 5 test scores were 90%, 80%, 82%, 75% and 88%. What must Rachel get on her next test
to meet her goal?
Data Analysis and Probability Interventions and Extensions 2- Green
Name
__
Date_______________
Score
/60
Use the chart for questions 1 and 2.
1. What is the probability that a randomly chosen student prefers assessment through a group project or
word problems?
Math Assessment Survey
Activity
Group
Projects
Keep a
Journal
Multiple
Choice
Word
Problems
Student
Response
57
18
35
10
2. What is the probability that a randomly chosen student will not want multiple-choice questions?
3. Tom has a dollar’s worth of dimes and a dollar’s worth of nickels in his pocket.
a. What is the probability he will randomly select a nickel from his pocket?
b. What is the probability he will randomly select a dime from his pocket?
4. Tia and her friends earned extra money by babysitting children in their neighborhood. Tia created a
table to show their earnings. Taylor noticed that Tia made a bunch of mistakes on everyone but Tia
herself. The group’s actual mean is $55. If three people made more money and three people less
money, how much did everyone make? In complete sentences, describe how you came up with your
answer.
Name
Tia
Sierra
Alexis
Jayla
Ja’Shauna
Diamond
Taylor
Earnings
$52
$49
$45
$60
$52
$65
$87
5. Robert’s grade for his college math class is made up of the average of 5 test scores. He has received a D,
C, B, B, and an A on his test. Show how the percent’s of these grades could give Robert either a C or B in the
class based on the actual percentages. Is there a way for him to get an A in the class with those grades?