State whether the events are independent or dependent.

choosing the color and size of a pair of shoes

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

choosing the winner and runner-up at a dog show

Elizabeth X.

Numerade Educator

An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different 1-scoop ice cream cones can a customer order?

Elizabeth X.

Numerade Educator

A bookshelf holds 4 different biographies and 5 different mystery novels. How many ways can one book of each type be selected?

A. 1

B. 9

C. 10

D. 20

Elizabeth X.

Numerade Educator

Lance’s math quiz has eight true-false questions. How many different choices for giving answers to the eight questions are possible?

Elizabeth X.

Numerade Educator

Pizza House offers three different crusts, four sizes, and eight toppings. How many different ways can a customer order a pizza?

Elizabeth X.

Numerade Educator

For a college application, Macawi must select one of five topics on which to write a short essay. She must also select a different topic from the list for a longer essay. How many ways can she choose the topics for the two essays?

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

choosing a president, vice-president, secretary, and treasurer for Student Council, assuming that a person can hold only one office

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

selecting a fiction book and a nonfiction book at the library

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

Each of six people guess the total number of points scored in a basketball game. Each person writes down his or her guess without telling what it is.

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

The letters A through Z are written on pieces of paper and placed in a jar. Four of them are selected one after the other without replacing any of them.

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

Tim wants to buy one of three different books he sees in a book store. Each is available in print and on CD. How many book and format choices does he have?.

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

A video store has 8 new releases this week. Each is available on videotape and on DVD. How many ways can a customer choose a new release and a format to rent?

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

Carlos has homework in math, chemistry, and English. How many ways can he choose the order in which to do his homework?

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

The menu for a banquet has a choice of 2 types of salad, 5 main courses, and 3 desserts. How many ways can a salad, a main course, and a dessert be selected to form a meal?

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

A baseball glove manufacturer makes gloves in 4 different sizes, 3 different types by position, 2 different materials, and 2 different levels of quality. How many different gloves are possible?

Elizabeth X.

Numerade Educator

State whether the events are independent or dependent.

Each question on a five-question multiple-choice quiz has answer choices labeled A, B, C, and D. How many different ways can a student answer the five questions?

Elizabeth X.

Numerade Educator

Abby is registering at a Web site. She must select a password containing six numerals to be able to use the site. How many passwords are allowed if no digit may be used more than once?

Elizabeth X.

Numerade Educator

Since the science books are to be together, they can be treated like one book and arranged with the music books. Use your answer to Exercise 19 and the Counting Principle to find the answer to the problem in the comic.

Elizabeth X.

Numerade Educator

Refer to the information about telephone area codes at the left.

How many area codes were possible before 1995?

Elizabeth X.

Numerade Educator

Refer to the information about telephone area codes at the left.

In 1995, the restriction on the middle digit was removed, allowing any digit in that position. How many total codes were possible after this change was made?

Elizabeth X.

Numerade Educator

How many ways can six different books be arranged on a shelf if one of the books is a dictionary and it must be on an end?

Elizabeth X.

Numerade Educator

In how many orders can eight actors be listed in the opening credits of a

movie if the leading actor must be listed first or last?

Elizabeth X.

Numerade Educator

How many different 5-digit codes are possible using the keypad shown at the right if the first digit cannot be 0 and no digit may be used more than once?

Elizabeth X.

Numerade Educator

Use the Internet or other resource to find the configuration of letters and numbers on license plates in your state. Then find the number of possible plates.

Elizabeth X.

Numerade Educator

Describe a situation in which you can use the Fundamental Counting Principle to show that there are 18 total possibilities.

Elizabeth X.

Numerade Educator

Explain how choosing to buy a car or a pickup truck and then selecting the color of the vehicle could be dependent events.

Elizabeth X.

Numerade Educator

The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club?

Elizabeth X.

Numerade Educator

Use the information on page 684 to explain how you can count the maximum number of license plates a state can issue. Explain how to use the Fundamental Counting Principle to find the number of different license plates in a state such as Oklahoma, which has 3 letters followed by 3 numbers. Also explain how a state can increase the number of possible plates without increasing the length of the plate number.

Elizabeth X.

Numerade Educator

How many numbers between 100 and 999, inclusive, have 7 in the tens place?

A. 90

B. 100

C. 110

D. 120

Elizabeth X.

Numerade Educator

A coin is tossed four times. How many possible sequences of heads or tails are possible?

F. 4

G. 8

H. 16

J. 32

Elizabeth X.

Numerade Educator

Prove that $4+7+10+\cdots+(3 n+1)=\frac{n(3 n+5)}{2}$ for all positive integers $n$.

Elizabeth X.

Numerade Educator

Find the indicated term of each expansion.

third term of $(x+y)^{8}$

Elizabeth X.

Numerade Educator

Find the indicated term of each expansion.

fifth term of $(2 a-b)^{7}$

Elizabeth X.

Numerade Educator

Edison is located at (9, 3) in the coordinate system on a road map. Kettering is located at (12, 5) on the same map. Each side of a square on the map represents 10 miles. To the nearest mile, what is the distance between Edison and Kettering?

Elizabeth X.

Numerade Educator

Solve each matrix equation.

$\left[\begin{array}{ll}{x} & {y}\end{array}\right]=\left[\begin{array}{ll}{y} & {4}\end{array}\right]$

Elizabeth X.

Numerade Educator

Solve each matrix equation.

$\left[\begin{array}{l}{3 y} \\ {2 x}\end{array}\right]=\left[\begin{array}{l}{x+8} \\ {y-x}\end{array}\right]$

Elizabeth X.

Numerade Educator