Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Advanced Algebra II: Activities and Homework » Homework: Permutations

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This collection is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy Busbee

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Homework: Permutations

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to permutations.

Exercise 1

The Film Club has four DVDs: Superman®, Batman®, The Incredibles®, and X-Men®. They are going to show two movies back-to-back for their Superhero End-of-School Blowout.

  • a. List all possible pairings. To keep it short, use letters to represent the movies: for instance, BX means Batman followed by X-Men. (XB is a different pairing, and should be listed separately.) BB, of course, means they will show Batman twice! Try to list them in a systematic way, to make sure you don’t miss any.
  • b. How many pairings did you list?
  • c. Now, list all possible pairings that do not show the same movie twice. Once again, try to list them in a systematic way, to make sure you don’t miss any.
  • d. How many pairings did you list?

Exercise 2

A new reality show, Famous American Rock Band, is going to choose lucky audience members to form a new Famous American Rock Band. There are 200 people in the audience.

  • a. First, the Lead Singer is chosen, and comes up onto the stage. How many possible choices are there?
  • b. Next, from the remaining audience members, a Lead Guitarist is chosen. How many possible choices are there?
  • c. Next, from the remaining audience members, a Rhythm Guitarist is chosen. How many possible choices are there?
  • d. Next, from the remaining audience members, a Bass Guitarist is chosen. How many possible choices are there?
  • e. Next, from the remaining audience members, a Pianist is chosen. How many possible choices are there?
  • f. Finally, from the remaining audience members, a Drummer is chosen. How many possible choices are there?
  • g. Multiply your answers in parts (a)–(f) to find the number of possible Rock Bands that could be created?
  • h. How could this calculation be expressed more compactly, with factorials?

Exercise 3

The school math club is going to elect a President, a Vice President, a Secretary, and a Treasurer. How many possible officer lists can be drawn up if...

  • a. There are only four people in the math club?
  • b. There are twenty people in the math club?

Exercise 4

A license plate consists of exactly eight characters. Assume that each character must be an uppercase letter, or a numerical digit.

  • a. How many possible license plates are there?
  • b. Now assume that you are also allowed to have blank spaces, which count as part of your eight letters. How many possible license plates are there?

Exercise 5

According to Robert de Boron’s version of the story, King Arthur’s Round Table was large enough to accommodate 50 chairs. One chair was always left empty, for the knight who would fulfill the Grail Quest. So, if 49 knights approach the table one day, how many different ways can they seat themselves?

Exercise 6

Invent, and solve, your own permutations problem. It should be a scenario that is quite different from all the scenarios listed above, but it should logically lead to the same method of solving.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks