Algebra II- Chapter 12- Test Review
Sections: Counting Principle
Permutations
Combinations
Probability
Name _________________________
Choose the letter of the term that best matches each statement or phrase.
1. _____ An illustration used to show the total number of possible outcomes.
A. circular permutations
2. _____ The number of possibilities of n objects, taken r at
B. combination a time and defined as C(n, r) =
( n − n r
!
)!
r !
C. fundamental counting principle
3. _____ The number of ways that n objects can be arranged in a circle and defined by (n – 1)!
4. _____ If one event can occur in m ways and another in n ways, then the number of ways that both can occur is m
n ways
5. _____ The desired outcome of an event
D. linear permutation
E. odds f. success g. tree diagram
6. _____ The number of possibilities of n objects arranged in a line and defined by P(n, r) =
( n n
−
!
r )!
7. _____ The ratio of the number of ways an event can succeed to the number of ways it can fail
How many ways can the letters of each word be arranged.
8. MONDAY 9. MOM 10. STEREO
Determine whether each situation involves a permutation or a combination.
11. choosing a class president, vice president, and secretary _______________
12. four tennis players from a group of nine _______________
13. eight toppings for ice cream _______________
State the probability of an event occurring, given the odds of the event.
14. 2:23 15. 3:5 16. 4:1 17. 9:7 18. 11:14
Evaluate each expression.
19. 1000:1
21.
11
C
3
22.
20
C
18
20.
8
C
2
23. (
9
C
3
)(
6
C
2
)

Algebra II- Chapter 12- Test Review
Solve.
24. The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many
passwords are possible if letters can be repeated any number of times?
25. In a bag there are 5 math questions and 4 science questions. Ardie picks a question from the bag. What are the
odds of not picking a science question?
26. How many 4-person bobsled teams can be chosen from a group of 9 athletes?
27. How many 4-digit positive even integers are there?
28. Ten points lie on a circle. How many line segments can be drawn between any two points ?
29. How many different ways can 4 different books be arranged on the shelf?
30. How many 5-sided polygons can be formed by joining any 5 of 11 points located on a circle?
31. A school club has 15 boys and 16 girls. How many different 6 person committees can be selected from the
membership if equal numbers of boys and girls are to be selected ?
32 . How many diagonals does a polygon with 12 sides have ?
33. An urn contains 8 white balls numbered 1 through 8 , 6 blue balls numbered 1 through 6, and 9 red balls
numbered 1 through 9. How many distinct groups of 6 balls can be selected to meet each condition? a.) All balls are red b.) Three are blue, 2 are white, and 1 is red c.) Two are blue, and 4 are red d.) Exactly 4 balls are white
34. How many ways can 8 members of a family be seated side-by-side in a movie theater if the father is seated in
the aisle seat?

Algebra II- Chapter 12- Test Review
35. What are the odds that a person chosen at random got a passing grade on an algebra test if the scores were 3
A’s, 4 B’s, 10 C’s, 2 D’s and 2 F’s?
36. How many ways can the first five letters of the alphabet be arranged if each is used only once?
37. How many license plate numbers consisting of three letters followed by three numbers are possible when
repetition is allowed?
38. How many license plates are possible using the information in problem 37 if no repetition is allowed?
39. From a dessert cart in a fine restaurant, customers are allowed to pick 3 desserts from the 10 that are displayed.
How many combinations are possible?
40. How many ways can 3 books be arranged on a shelf if chosen from a selection of 7 different books?
41. A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each
has a main dish, a salad, and a dessert?
42. One bag of candy gummy fish contains 15 red gummy fish, 10 yellow gummy fish, and 6 green gummy fish.
Find the probability of each selection. a.) picking a red gummy fish b.) not picking a yellow gummy fish c.) picking a green gummy fish d.) not picking a red gummy fish
43. How many 5-digit even numbers can be formed using the digits 4,6,7,2,8 if digits can be repeated any number
of times ?
44. How many ways can 8 campers be seated around a campfire?
45. State the odds of an event occurring, given the probability of the event. a.) 4
11 b.) 2
3 c.) 5
99 d.) 1
1000 e.) 5
16 f.) 3
95
46. In a group of 10 people, each person shakes hands with everyone else once. How many handshakes are there?
(this is a famous problem)

Algebra II- Chapter 12- Test Review
47.
For next year’s schedule of classes, mathematics, English, history and science are scheduled during the first four period of the day. Your schedule is randomly selected by a computer. Find the probability that English, math, science and history will be scheduled in that order.
48.
Seven letters are chosen, one at a time, at random from those in the word ENGLISH. a.) Find the probability that they will be chosen in alphabetical order. b.) Find the probability that the first letter will be a vowel.
49.
Consider a state lottery which randomly selects 6 numbered balls from a bin. The balls are numbered from 1 to
52. To win the jackpot, a player must match all 6 balls, in any order. Determine the probability of winning the jackpot (matching all 6 numbers) for a person who buys one ticket.
50.
To increase the difficulty of the lottery (and also the size of the jackpot), the state decides to label the last ball which is drawn as the “Final Ball.” To win the jackpot, a ticket must match the first five balls in any order, and the Final Ball.
Determine the probability of winning the jackpot for a person who buys one ticket.

Algebra II- Chapter 12- Test Review
Create Pascal’s Triangle Below:
Use the binomial theorem to write the binomial expansion.
51.) ( x – 10 ) 5
52.) (x + 3y) 7

Algebra II- Chapter 12- Test Review
53.)
Find the indicated probability. State whether A and B are mutually exclusive.
54.
( )
( )
=
=
0.3
0.55
P A
(
(
or B
and B
) =
)
0.85
= ______
55.
( )
( )
=
=
40%
_____
P A or B
(
( ) = 60%
and B
) = 12%
Mutually exclusive: ___________
Find P(A’)
Mutually exclusive: ___________
56 .
( )
=
1
5
( )
' = ____
Choosing Cards – For problems 4 through 7: ONE card is randomly drawn from a standard
52-card deck. Find the probability of the given event. State your answer in fractions .
57. An queen or a heart = ___________ 58. A face card and a club = ________
59. Not an ace = _________ 60. Less than or equal to four (an ace is one) = _______
61.
You randomly select two cards from a standard deck of 52 cards. What is the probability that
the first card that you select is a jack or an ace and the second card is an ace, jack, or queen
if you replace the first card before selecting the second? – State your answer in rounded to
four decimals .

Algebra II- Chapter 12- Test Review
62 . In exercise 61, what is the probability if you DO NOT replace the first card before selecting
the second? – State your answer in rounded to four decimals .
63. The probability of a tourist visiting an area cave is .70 and of a tourist
visiting a nearby park is .60. The probability of visiting both places on the same day is .40.
The probability that a tourist visits an area cave or a nearby park on the same day is:
64. A drawer contains 7 pairs of white socks and 4 pairs of gray socks. You randomly select 3
pairs of socks from the drawer. Find the probability that the 3 pairs that you selected are
white.
Round your answer to three decimals.
Use the below information for problems 65-66.
Marbles in a jar - A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles. Find the probability of choosing the given marbles from the jar. Answer with decimals rounded to 3 places.
Part a) With replacement
Part b) Without replacement
65.
red, then blue 66.
white, then white 67.
red, then white, then red
65 a) _______
b) _______
66 a) _______
b) _______
67 a) _______
b) _______
68. Angela usually rushes to make it to the bus stop in time to catch the school bus, and will
often miss the bus if it is early. The bus comes early to Angela’s stop 28% of the time.
What is the probability that the bus will come early at least once during a 5 day school
week?
69. A tennis player wins a match 55% of the time when she serves first and 47% of the time
when her opponents serves first. The player who serves first is determined by a coin toss
before the match. What is the probability that the player wins a given match?

Algebra II- Chapter 12- Test Review
70. A card is drawn randomly from a standard 52-card deck. Find the probability of drawing a
red face card.
71.
A school club has 5 freshman, 3 sophomores, 2 seniors and 2 juniors. How many
different 8 person committees can be formed if equal numbers of freshman, sophomores,
juniors and seniors are to be selected ?
72.
If the probability of an event occurring is 8
25
, what are the odds that the event will occur?
73.
If the odds of winning a contest are 1:553, what is the probability of losing the contest?
74.
A coin purse contains 5 pennies, 7 nickels, and 8 dimes. A coin is selected at random. Find
the probability that the coin is a dime.
75.
Penn State University holds a lottery for spaces in their dormitories for sophomores. They
have a total of 1,580 rooms available for sophomores. If you are one of 2,348 students
entering the lottery for a dormitory room, what are the odds that you will have to look
elsewhere for housing?
76.
In a game of Go Fish you choose 1 card from player to your right. Your hand contains:
K ♣ Q ♦ 10 ♦ 3 ♠ 2 ♥
The player to your right is holding:
J ♦ 10 ♣ 5 ♥ 3 ♦ A ♠
When you draw one card from the person to your right without seeing his cards, what is the probability that you will create a pair in your hand? (A pair consists of two cards that are the same number/face card).

Algebra II- Chapter 12- Test Review
77.
The table at right gives the results of rolling one die 50 times. What is the experimental
probability of rolling a 3?
Roll 1 2 3 4 5 6
Number of occurrences 10 12 9 3 11 5
78.
The target at right is used for a game of darts. The inner circle has a radius of 1” and each ring has a radius width of 1”. If a dart has the same chance of landing at any point in the square, what is the probability of landing your first dart in either of the rings worth 30 or 40 points?
10
20
30
40
50
79.
A bag of Hershey kisses contains 3 milk chocolate, 10 dark chocolate, and 15 chocolate almond kisses. What is the probability of drawing a milk chocolate or a dark chocolate kiss?
80. Use the data to complete the problem BY HAND, show all your work for full credit!
46, 18, 64, 28, 48, 18
MEAN: __________
RANGE: _________
MEDIAN:__________
VARIANCE: ________
MODE: _____________
STANDARD DEV: _________
Min: ______ Q
1
: ______ Q
2
: ______ Q
3
: _______ Max: ______ IQR: __________
Use the information you just found to draw a box-and-whisker plot

Algebra II- Chapter 12- Test Review
81.
The following statistics were produced at the end of a week at a weight loss center indicating
pounds lost.
mean = 5 lbs.
median = 7 lbs.
mode = 4 lbs. first quartile = 2 lbs. third quartile = 8.5 lbs. standard deviation = 0.5 lbs.
Which of the following statements are correct?
I.
One quarter of weight watchers lost 2 pounds or less
II.
The middle 50% of the weight watchers lost between 2 and 8.5 pounds
III.
The most common weight loss was 4 pounds.
82.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III
The boxplots above summarize two sets of data, A and B. Which of the following must be
true?
I.
Set B contains more observations than Set A
II.
Set A has a larger range than Set B
III.
Set A and Set B have the same median.
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III

Algebra II- Chapter 12- Test Review