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Middle School: Combinations and Permutations

In grades 6-8, discrete math problems are likely to explore permutations and combinations: see for example Back Yard Trees (how many different quadrilaterals can be formed by joining any four of nine trees?), or Mr. Carmel's Party Plan (help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes).

Combinatorics problems appropriate for middle-school students are listed below.

For information elsewhere on our site, see Permutations and Combinations, from the Dr. Math FAQ. Answers at the high-school level in the Dr. Math archives may also be useful to middle-school students; see Permutations and Combinations. For relevant sites on the Web, browse and search Combinatorics: Permutations and Combinations in our Internet Mathematics Library; to find middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.

Access to these problems requires a Membership.

Back Yard Trees - Judy Ann Brown
active problem Pre-Algebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees? ... more>>

Club Competition - Suzanne Alejandre
active problem Pre-Algebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition. ... more>>

Coding Conundrums - Mary DeYoung & class
active problem Pre-Algebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle. ... more>>

Even Number Puzzle - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. How many even four-digit whole numbers exist such that the thousands digit is odd, and all four digits are different? ... more>>

Fall Festival Frolic - Judy Ann Brown
active problem Pre-Algebra, 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
active problem Pre-Algebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins? ... more>>

Locker Combinations - Judy Ann Brown
active problem Pre-Algebra, difficulty level 4. In this counting problem you will need to determine the total number of possible locker combinations. ... more>>

Mr. Carmel's Party Plan - Judy Ann Brown
active problem Pre-Algebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes. ... more>>

Pegging Possibilities - Michael Urbut
active problem Pre-Algebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game. ... more>>

Rampaging Reindeer - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. How many different ways can Santa's reindeer be arranged? ... more>>

Seating Arrangements - Judy Ann Brown
active problem Pre-Algebra, difficulty level 3. Four new students arrive in Mrs. Brown's homeroom. After a few minutes she turns to them and says, "There are 1680 ways that you can sit in the empty seats." How many empty seats are there in the room? ... more>>

Student Council Elections - Judy Ann Brown
active problem Pre-Algebra, difficulty level 4. Find the number of ways names can be arranged on the student council ballot, and figure the odds that a brother and sister will both be listed first in their respective races. ... more>>

Trick-or-Treat Route - Judy Ann Brown
active problem Pre-Algebra, difficulty level 4. Which of the many possible routes should the Anderson children take on their Halloween trek? ... more>>

Ursala is Undecided - Melissa Kennedy, Ethel Breuche
active problem Discrete Math, difficulty level 1. Poor Undecided Ursala has many paths to choose to get from point A to point S. Exactly how many paths does she have a choice of taking? ... more>>

Where Should I Sit? - Judy Ann Brown
Middle School, difficulty level 3. On Monday three new students arrived in Mrs. King's homeroom... How many empty seats were there in Mrs. King's room? ... more>>

Wraparound Universe - Jeff Weeks
active problem Pre-Algebra, difficulty level 4. Explore the game of tic-tac-toe using a cylindrical tic-tac-toe board. ... more>>

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