Deck 5: Possibilities and Probabilities

Question 1

Which of the following is false?

A) $13 !=13 \cdot 12 \cdot 11 \cdot 10 !$
B) $8^{P_{2}}=28$
C) $\left(\begin{array}{l}5 \\ 2\end{array}\right)=10$
D) $\left(\begin{array}{c}15 \\ 4\end{array}\right)=\frac{15 \cdot 14 \cdot 13 \cdot 12}{4 \cdot 3 \cdot 2}$

Answer 1

$8^{P_{2}}=28$

Question 2

A multiple choice test has 10 questions with 4 choices for each question. The number of ways a student can answer all 10 questions is

A) $10 \cdot 4$
B) 410
C) $10^{4}$
D) $10+4$

Answer 2

410

Question 3

Two restaurants are to be built at locations selected from a choice of 11 locations. The number of ways selecting the locations for the two restaurants is

A) $\frac{11 !}{2}$
B) $11 \cdot 11$
C) $\frac{11 \cdot 10}{2}$
D) $11 \cdot 10$

Answer 3

$\frac{11 \cdot 10}{2}$

Question 4

In an 8-horse race, the number of ways that 3 horses can finish first, second, and third (order matters) is given by

A) $8 \cdot 3$ .
B) $8^{3}$ .
C) $8 \cdot 7 \cdot 6$
D) $\frac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1}$

Question 5

The probability of selecting a defective component from 20 components, 3 of which are defective, is $\frac{3}{20}$ . This is an example of

A) the classical probability concept.
B) the frequency interpretation of probability.
C) the law of large numbers.
D) subjective probability.

Question 6

A company employs 40 skilled and 30 unskilled workers. Twenty -five of the skilled workers and 17 of the unskilled are college graduates. If an employee of the company is selected at random, the probability that the person picked will not be a college graduate is

A) $\frac{2}{5}$ .
B) $\frac{25}{70}$ .
C) $\frac{12}{28}$ .
D) $\frac{17}{70}$ .

Question 7

Which of the following is not true of the symbol $\left(\begin{array}{c}11 \\ 3\end{array}\right)$ ?

A) It is used when order does not matter.
B) Its value is less than $11 P_{3}$ .
C) It is the number of 3 letter words that can be formed from 11 letters.
D) It is the number of 3 person committees that can be formed from a group of 11 people.

Question 8

In the past eight Friday nights, a student has gone to the same rock music club on five occasions. The claim that the probability is $\frac{5}{8}$ that the student will attend the same club next Friday is based on

A) the classical probability concept.
B) the frequency interpretation of probability.
C) the law of large numbers.
D) subjective probability.

Question 9

A student has time to see four films on his vacation. If he is selecting the movies from a total of nine choices, how many ways can he choose the films?

A) $9 \cdot 4$
B) $9 \cdot 8 \cdot 7 \cdot 6$
C) $\frac{9 !}{4 !}$
D) $\frac{9 \cdot 8 \cdot 7 \cdot 6}{4 \cdot 3 \cdot 2 \cdot 1}$

Question 10

A student has seven items of living room furniture and room for five items in his living room. Assuming that any of the seven items can be placed in any of the five locations, in how many ways can the student arrange his living room with the furniture?

A) $\left(\begin{array}{l}7 \\ 5\end{array}\right)$
B) $7 \cdot 6$
C) $7 \cdot 6 \cdot 5 \cdot 4 \cdot 3$
D) $7 \cdot 5$

Question 11

A student can play 0,1 , or 2 hours of racquetball on any given night. Construct a tree diagram to determine the number of ways that in three nights he can play for a total of four hours.

Question 12

A student can play 0, 1, or 2 hours of racquetball on any given night. Construct a tree diagram to determine the number of ways that in three nights he can play for a total of five hours.

Question 13

Give the number of ways a student can mark her answers to a multiple choice test if there are eight questions with three choices each.

Question 14

Give the number of ways a student can mark her answers to a multiple choice test if there are three questions with eight choices each

Question 15

Give the number of ways a student can mark her answers to a multiple choice test if there are 10 questions with four choices each for the first three questions and five choices each for the next seven questions.

Question 16

There are six baseball teams in the American League's Eastern division. In how many ways can:}
-three teams finish first, second, and third?

Question 17

There are six baseball teams in the American League's Eastern division. In how many ways can:}
-all six teams finish first through sixth?

Question 18

A new campus project requires a committee of 5 students which will include 2 seniors and 3 juniors. There are 6 available seniors and 8 available juniors.
-In how many ways can the juniors be chosen for the committee?

Question 19

A new campus project requires a committee of 5 students which will include 2 seniors and 3 juniors. There are 6 available seniors and 8 available juniors.
-In how many ways can the required committee be chosen?

Question 20

A new campus project requires a committee of 5 students which will include 2 seniors and 3 juniors. There are 6 available seniors and 8 available juniors.
-In how many ways can the committee be chosen from the available students if there are no restrictions on the number of juniors or seniors on the committee?

Question 21

A shipment of 12 television sets contains one that is damaged. In how many ways can an inspector choose 3 of the televisions to inspect so that:
-the defective item is not included?

Question 22

A shipment of 12 television sets contains one that is damaged. In how many ways can an inspector choose 3 of the televisions to inspect so that:
-the defective item is included?

Question 23

A balanced die is rolled. Find the probability of getting:
-a value of at least two.

Question 24

A balanced die is rolled. Find the probability of getting:
-an odd number.

Question 25

Two cards are drawn from a well-shuffled deck of 52 playing cards.}
-What is the probability of getting two jacks?

Question 26

Two cards are drawn from a well-shuffled deck of 52 playing cards.}
-What is the probability of getting two clubs?

Question 27

Two cards are drawn from a well-shuffled deck of 52 playing cards.}
-What is the probability of getting an ace and a king?

Question 28

A student is planning the music she will play at a party. If she has 15 record albums and wants to select 6 to play, in how many ways can she select the albums if she believes that:
-the order of the records matter?

Question 29

A student is planning the music she will play at a party. If she has 15 record albums and wants to select 6 to play, in how many ways can she select the albums if she believes that:

-the order of the records does not matter?

Question 30

If 3 of 16 tax returns contain errors, and 7 of them are randomly chosen for audit, what is the probability that:
-exactly two of the returns with errors are audited?

Question 31

If 3 of 16 tax returns contain errors, and 7 of them are randomly chosen for audit, what is the probability that:
-all three of the returns with errors are audited?

Question 32

If 3 of 16 tax returns contain errors, and 7 of them are randomly chosen for audit, what is the probability that:
-none of the returns with errors is audited?

Question 33

Two vice presidents are to be selected from the division managers in a certain company. If there are 9 division managers, in how many ways can the vice presidents be selected?

Question 34

After two vice presidents are selected from 9 division managers, 3 other promotions will be granted. From the remaining division managers, how many ways can the new promotions be granted?

Question 35

Two families, each consisting of a husband, a wife, two sons, and one daughter, are planning to see a movie together and sit together in the same row. In how many ways can they be seated if:
-each family is to sit together?

Question 36

Two families, each consisting of a husband, a wife, two sons, and one daughter, are planning to see a movie together and sit together in the same row. In how many ways can they be seated if:
-all the males are to sit together and all of the females are to sit together?

Question 37

Two families, each consisting of a husband, a wife, two sons, and one daughter, are planning to see a movie together and sit together in the same row. In how many ways can they be seated if:
-all of the children are to sit together and all of the adults are to sit together?

Question 38

How many permutations are there of the letters in the word "distinction"?

Question 39

In how many ways can 12 persons be arranged in a circle?

Question 40

A cable TV company has 10 channel offerings. One option is that a subscriber may select any four channels. In how many ways can a subscriber make his/her selection?

Question 41

I have 11 shirts, but only four hangers. In how many ways can I choose four of the shirts to hang in which the arrangement of the shirts in my closet makes a difference to me?

Question 42

A group of investors wants to hire a team of 4 accountants and 2 financial planners. If the investors are considering 8 accountants and 5 financial planners:}
-how many six-person teams can be hired under the given conditions?

Question 43

A group of investors wants to hire a team of 4 accountants and 2 financial planners. If the investors are considering 8 accountants and 5 financial planners:}
-how many six-person teams can be hired if no attention is paid to profession?

Question 44

An accounting firm is selecting three accounts to audit out of a total of 11 accounts. The number of ways the firm can select the three accounts is given by $11 \cdot 10 \cdot 9$ .

Question 45

The number of three person committees that can be formed from eight people is the same as the number of three-letter words that can be formed from the letters a, b, c, d, e, f, g, h with no repetitions.

Question 46

The probability of rolling a three in one roll of an ordinary die is $\frac{1}{6}$ . This is an example of the frequency interpretation of probability.

Question 47

The expression 7 ! 3 ! is equal to 10 !.

Question 48

The expression 11 ! is equal to $\frac{12 !}{12}$ .

Question 49

The number of six-letter words that can be formed from the word OBJECT is 6!

Question 50

The multiplication of choices principle states that if an experiment is repeated again and again, the proportion of successes will tend to approach the probability that any one outcome will be a success.

Question 51

A magazine reader wants to subscribe to three magazines from a choice of eight magazines. The number of ways this can be done is $\frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{3 \cdot 2 \cdot 1}$

Question 52

The number of seven-digit phone numbers that can be formed that begin with 353 with not all of the last four digits 0 is 94 .

Question 53

The number of ways that 4 students can be selected from 30 students in a class to fill 4 seats (if order matters) is $\frac{30 \cdot 29 \cdot 28 \cdot 27}{4 \cdot 3 \cdot 2 \cdot 1}$

Question 54

The number of five-player basketball teams that can be formed from a group of 11 players is _______.

Question 55

The value of $\left(\begin{array}{l}7 \\ 3\end{array}\right)$ is _______.

Question 56

The value ${ }_{7} P_{3}$ is _______.

Question 57

The symbol $\left(\begin{array}{l}20 \\ 13\end{array}\right)$ can be rewritten symbolically as _______.

Question 58

The probability of selecting a face card in one draw of a card from an ordinary deck is _______.

Question 59

The factorial notation for ${ }_{7} P_{7}$ is _______.

Question 60

The factorial notation for ${ }_{8} P_{5}$ is _______.

Question 61

A restaurant menu has eight main courses, five appetizers, six desserts, and four beverages. The number of ways that a patron can select a meal with one appetizer, one main course, one dessert, and one beverage is _______.

Question 62

If the president is considering the elimination of seven federal programs but is selecting only three of the seven to eliminate, the number of ways he can select the programs is _______.

Question 63

A woman who is furnishing her apartment is selecting a sofa, a lounge chair, and a bookcase. If she has five sofas, eight lounge chairs, and three bookcases to choose from, the number of ways that she can select the furniture is _______.