Skip to content Skip to navigation

Connexions

You are here: Home » Content » Probability Homework -- Homework: Permutations and Combinations

Navigation

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 module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Advanced Algebra II: Activities and Homework"

    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 module is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy BusbeeAs a part of collection: "Advanced Algebra II: Activities and Homework"

    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.
 

Probability Homework -- Homework: Permutations and Combinations

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

Summary: This module provides practice problems related to permutations and combinations.

Exercise 1

The comedy troupe Monty Python had six members: John Cleese, Eric Idle, Graham Chapman, Michael Palin, Terry Gilliam, and Terry Jones. Suppose that on the way to filming an episode of their Flying Circus television show, they were forced to split up into two cars: four of them could fit in the Volkswagen, and two rode together on a motorcycle. How many different ways could they split up?

  • a. List all possible pairs that might go on the motorcycle. (Note that “Cleese-Idle” and “Idle-Cleese” are the same pair: it should be listed once, not twice.)
  • b. List all possible groups of four that might ride in the car. (Same note.)
  • c. If you listed properly, you should have gotten the same number of items in parts (a) and (b). (After all, if Cleese and Idle ride on the motorcycle, we know who is in the car!) This number is “6 choose 2,” or 6262 size 12{ left ( matrix { 6 {} ## 2 } right )} {}. It is also “6 choose 4,” or 6464 size 12{ left ( matrix { 6 {} ## 4 } right )} {}. Given that they came out the same, 103103 size 12{ left ( matrix { "10" {} ## 3 } right )} {} should come out the same as what?.
  • d. Write an algebraic generalization to express the rule discussed in part (c).

Exercise 2

A Boston Market® Side Item Sampler® allows you to choose any three of their fifteen side items. How many possible Side Item Samplers can you make?

  • a. To answer this combinations question, begin with a related permutations question. Suppose you had three plates labeled Plate 1, Plate 2, and Plate 3, and you were going to put a different side item in each plate.
    • i. How many items could you put in Plate 1?
    • ii. For each such choice, how many items could you put in Plate 2?
    • iii. For each such choice, how many items could you put in Plate 3?
    • iv. So, how many Plate 1– Plate 2 – Plate 3 permutations could you create?
  • b. The reason you haven’t answered the original question yet is that, in a real Side Item Sampler, the plates are not numbered. For instance, “Sweet Corn–Mashed Potatoes–Creamed Spinach” is the same meal as “Creamed Spinach–Mashed Potatoes–Sweet Corn.” So...in the space below, list all the possible arrangements of just these three side items.
  • c. How many possible arrangements did you list? (In other words, how many times did we originally count every possible meal?)
  • d. Divide your answer to a(iv) by your answer to (b) to find out how many Side Item Samplers can be created.

Exercise 3

How many three-note chords can be made by...

  • a. Using only the eight “natural” notes (the white keys on a piano)?
  • b. Using all twelve notes (black and white keys)?

Exercise 4

The United States Senate has 100 members (2 from each state). Suppose the Senate is divided evenly: 50 Republicans, and 50 Democrats.

  • a. How many possible 3-man committees can the Republicans make?
  • b. Express your answer to part (a) in terms of factorials.
  • c. How many possible 47-man committees can the Republicans make?
  • d. How many 10-man committees can the Democrats make?
  • e. How many committees can be formed that include 5 Democrats and 5 Republicans?

Exercise 5

Invent, and solve, your own combinations 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.

Content actions

Download module as:

PDF | More downloads ...

Add 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