Exercises 8.4 Exercises
1.
A boy owns 2 pairs of pants, 3 shirts, 8 ties, and 2 jackets. How many different outfits can he wear to school if he must wear one of each item?
2.
At a restaurant you can choose from 3 appetizers, 8 entrees, and 2 desserts. How many different three-course meals can you have?
3.
How many three-letter "words" can be made from 4 letters "FGHI" if
repetition of letters is allowed
repetition of letters is not allowed
64
24
4.
How many four-letter "words" can be made from 6 letters "AEBWDP" if
repetition of letters is allowed
repetition of letters is not allowed
5.
All of the license plates in a particular state feature three letters followed by three digits (e.g. ABC 123). How many different license plate numbers are available to the state's Department of Motor Vehicles?
6.
A computer password must be eight characters long. How many passwords are possible if only the 26 letters of the alphabet are allowed? Assume the password is not case-sensitive.
7.
A California license plate starts with a digit other than 0, followed by three capital letters, followed by three more digits (0 through 9)
How many different California license plates are possible?
How many different California license plates start with a 5 and end with a 9?
How many different California license plates have no repeated symbols? (all the digits and all the letters are different)
158,184,000
1,757,600
70,761,600
8.
A computer password consists of four letters (A through Z) followed by a single digit (0 through 9). Assume that the passwords are case sensitive (i.e., uppercase letters are considered different from lowercase letters).
How many passwords are possible?
How many passwords start with a capital Z?
How many passwords do not start with either z or Z?
How many passwords have no Zs in them (uppercase or lowercase)
9.
A restaurant offers a menu consisting of three different appetizers, two different soups, four salads, and nine main courses
How fixed-price lunch consists of a choice of appetizer, salad, and main course. How many different lunch meals are possible?
A fixed-price dinner consists of a choice of appetizer, a choice of soup or salad, and a main course. How many different dinner meals are possible?
108
162
10.
A pianist plans to play 4 pieces at a recital. In how many ways can she arrange these pieces in the program?
11.
In how many ways can first, second, and third prizes be awarded in a contest with 210 contestants?
12.
Seven Olympic sprinters are eligible to compete in the 4 x 100 m relay race for the USA Olympic team. How many four-person relay teams can be selected from among the seven athletes?
13.
Twenty newspapers are competing for three awards in journalism. No paper can receive more than one award. In how many ways can the awards be given, if
the awards are identical?
the awards are all different?
1,140
6,840
14.
A college is forming a task force with four faculty members and three students. If there are 20 faculty members and 10 students that are being considered, in how many ways can the task force be formed?
15.
A computer user has downloaded 25 songs using an online file-sharing program and wants to create a CD-R with ten songs to use in his portable CD player. If the order that the songs are placed on the CD-R is important to him, how many different CD-Rs could he make from the 25 songs available to him?
16.
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
17.
In the early twentieth century, proponents of the Second Viennese School of musical composition (including Arnold Schönberg, Anton Webern and Alban Berg) devised the twelve-tone technique, which utilized a tone row consisting of all 12 pitches from the chromatic scale in any order, but with not pitches repeated in the row. Disregarding rhythm and octave changes, how many tone rows are possible?
18.
In how many ways can 3 students be chosen from a group of 30 to attend a conference?19.
In how many ways can 4 pizza toppings be chosen from 12 available toppings?
20.
At a baby shower 17 guests are in attendance and 5 of them are randomly selected to receive a door prize. If all 5 prizes are identical, in how many ways can the prizes be awarded?
21.
In the 6/50 lottery game, a player picks six numbers from 1 to 50. How many different choices does the player have if order doesn’t matter?
22.
In a lottery daily game, a player picks three numbers from 0 to 9. How many different choices does the player have if order doesn’t matter?
23.
A jury pool consists of 27 people. How many different ways can 11 people be chosen to serve on a jury and one additional person be chosen to serve as the jury foreman?
24.
The United States Senate Committee on Commerce, Science, and Transportation consists of 23 members, 12 Republicans and 11 Democrats. The Surface Transportation and Merchant Marine Subcommittee consists of 8 Republicans and 7 Democrats. How many ways can members of the Subcommittee be chosen from the Committee?