Algebra 2 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities

Functions

Statistics

SOL Review Materials
AII.12
The student will compute and distinguish between permutations and combinations and use technology for applications.
Essential Knowledge and Skills 
  • Compare and contrast permutations and combinations.
  • Calculate the number of permutations of n objects taken r at a time.
  • Calculate the number of combinations of n objects taken r at a time.
  • Use permutations and combinations as counting techniques to solve real-world problems.
Essential Understandings
  • The Fundamental Counting Principle states that if one decision can be made n ways and another can be made m ways, then the two decisions can be made nm ways.
  • Permutations are used to calculate the number of possible arrangements of objects.
  • Combinations are used to calculate the number of possible selections of objects without regard to the order selected.
Vertical Articulation
  1. SOL AFDA.6 - calculate probabilities a) conditional prob; b) dep/indep events; c) add/mult rules; d) counting techniques (permutations/combinations); Law of Large Numbers
Instructional Materials
  1. VDOE ESS Lesson: Combinations and Permutations - Statistics (PDF) - Counting using permutations and combinations (Word)
  2. Warm-up: Permutations and Combinations (flipchart)
  3. Activity: Permutations (doc)
  4. Activity: Combinations (doc)
  5. Notes: Permutations and Combinations (ppt)
Real World Lessons
Practice
  1. VDOE ESS - Permutation Activity (pdf)
  2. VDOE ESS - Combination Activity (pdf)
  3. VDOE ESS - Counting Exploration (pdf)
  4. Worksheet: Permutations and Combinations (doc)
  5. Worksheet: Permutations and Combinations MC (pdf)
Self-Assessments
  1. Permutations and Combinations Mini-Quiz
Skills
  1. JMU Pivotal Question: Permutations (doc)
  2. JMU Pivotal Question: Combinations (doc)
Videos
  1. PH Using Permutations
  2. PH Evaluating Combinations
  3. PH Using Combinations
Explore Learning
  1. Binomial Probabilities - Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation.
  2. Permutations - Experiment with permutations of a number of letters represented by letter tiles selected at random from a box. Count the permutations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.
  3. Permutations and Combinations - Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.
Websites
  1. Notes: Using the TI to find permutations
  2. Notes: Using the TI to find combinations
  3. Notes: Fundamental Counting Principle
  4. Notes: Permutations at Regentsprep.com
  5. PH Permutations and Combinations Quiz
  6. PH Permutations and Combinations #2 Quiz
Common Core Standards
S-CP.9