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Combinations

The problems in this section explore combinations defined as a way to select one or more elements from a set without regard to the order of selection.
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Counting Principles: Combinations
The closest match in our Ask Dr. Math archives:
Middle School Archive
NCTM Standards:
Data Analysis & Probability Standard for Grades 68
Access to these problems requires a Membership.

Basic Breakfast Buffet
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How many days could Linnea, Joel, Karl, and Jakob stay at the hotel
before one of them would
have to repeat one of the breakfasts?
... more>>

Change Woes
 suggested by a Western Oregon University mentor

PreAlgebra, difficulty level 3. What coins did Lacey have before her money was mixed up with her
brother's?
... more>>

Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
... more>>

Colors of the Olympic Rings
 Suzanne Alejandre

PreAlgebra, difficulty level 2. If we categorize all the flags of the world by the combination of the
Olympic ring colors
that appear in them, how many categories would we have?
... more>>

Eminen
 Annie Fetter

Geometry, difficulty level 3. Figure out what size squares will tile a rectangle.
... more>>

Fall Festival Frolic
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags?
... more>>

Flipping Over Pennies
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins?
... more>>

Mr. Carmel's Party Plan
 Judy Ann Brown

PreAlgebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes.
... more>>

Part of a Rectangle
 Annie Fetter

Geometry, difficulty level 3. Given the area of part of a rectangle, find the area of the whole thing.
... more>>

Pegging Possibilities
 Michael Urbut

PreAlgebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
... more>>

Rampaging Reindeer
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different ways can Santa's reindeer be arranged?
... more>>

Totolospi
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Calculate the probability of advancing on a toss when playing the game
Totolospi.
... more>>

Wraparound Universe
 Jeff Weeks

PreAlgebra, difficulty level 4. Explore the game of tictactoe using a cylindrical tictactoe board.
... more>>
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