# AII.12 - Permutations and Combinations

AII.12  The student will compute and distinguish between permutations and combinations.

### BIG IDEAS

• I can pick the winning combination of numbers to win the lottery, list unique combinations of numbers and letters for license plates, design communication networks, and utilize cryptography for network security.
• I will be able to differentiate between permutations and combinations in order to apply them appropriately to various situations.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AII.12 Understanding

·  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.

·  A permutation is the number of possible ways to arrange a group of objects without repetition and when order matters (e.g., the outcome 1, 2, 3 is different from the outcome 3, 2, 1 when order matters; therefore, both arrangements would be included in the possible outcomes).

·  A combination is the number of possible ways to select or arrange objects when there is no repetition and order does not matter (e.g., the outcome 1, 2, 3 is the same as the outcome 3, 2, 1 when order does not matter; therefore, both arrangements would not be included in the possible outcomes).

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  AII.121  Compare and contrast permutations and combinations.

·  AII.122  Calculate the number of permutations of n objects taken r at a time.

·  AII.124  Use permutations and combinations as counting techniques to solve practical problems.

·  AII.125  Calculate and verify permutations and combinations using a graphing utility.

·  AII.121  Compare and contrast permutations and combinations.

·  AII.123  Calculate the number of combinations of n objects taken r at a time.

·  AII.124  Use permutations and combinations as counting techniques to solve practical problems.

·  AII.125  Calculate and verify permutations and combinations using a graphing utility.

### KEY VOCABULARY

permutation, combination, Fundamental Counting Principle

Updated: Aug 23, 2018