# AII.12 and *AII.12 - Permutations and Combinations

AII.12    The student will compute and distinguish between permutations and combinations and use technology for applications.

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

Bloom's Level:  Apply, Analyze

### 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

• 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.

·  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

Permutations

All.121  Compare and contrast permutations and combinations.

·  AII.121  Compare and contrast permutations and combinations.

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

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

All.124  Use permutations and combinations as counting techniques to solve real-world problems.

·  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.

Combinations

All.121  Compare and contrast permutations and combinations.

·  AII.121  Compare and contrast permutations and combinations.

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

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

All.124  Use permutations and combinations as counting techniques to solve real-world problems.

·  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: Oct 27, 2017