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 realworld 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 
 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 
 VDOE ESS Lesson: Combinations and Permutations  Statistics (PDF)  Counting using permutations and combinations (Word)
 Warmup: Permutations and Combinations (flipchart)
 Activity: Permutations (doc)
 Activity: Combinations (doc)
 Notes: Permutations and Combinations (ppt)

Real World Lessons 

Practice 
 VDOE ESS  Permutation Activity (pdf)
 VDOE ESS  Combination Activity (pdf)
 VDOE ESS  Counting Exploration (pdf)
 Worksheet: Permutations and Combinations (doc)
 Worksheet: Permutations and Combinations MC (pdf)

SelfAssessments 
 Permutations and Combinations MiniQuiz

Skills 
 JMU Pivotal Question: Permutations (doc)
 JMU Pivotal Question: Combinations (doc)

Videos 
 PH Using Permutations
 PH Evaluating Combinations
 PH Using Combinations

Explore
Learning 
 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.
 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.
 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 
 Notes: Using the TI to find permutations
 Notes: Using the TI to find combinations
 Notes: Fundamental Counting Principle
 Notes: Permutations at Regentsprep.com
 PH Permutations and Combinations Quiz
 PH Permutations and Combinations #2 Quiz

Common Core
Standards 
