#### Math - 2017-18

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

**Bloom's Level: ** Apply, Analyze

*Adopted: 2009*

### 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.12_{1} **Compare**
and **contrast** permutations and
combinations.

· AII.12_{1} **Compare**
and **contrast** permutations and
combinations.

All.12_{2} **Calculate**
the number of permutations of n objects taken r at a time.

· AII.12_{2} **Calculate**
the number of permutations of *n *objects taken *r *at a time.

All.12_{4} **Use**
permutations and combinations as counting techniques to **solve** real-world problems.

· AII.12_{4} **Use** permutations and combinations as counting techniques to
**solve** practical problems.

· AII.12_{5} **Calculate** and **verify**
permutations and combinations using a graphing utility.

__Combinations __

All.12_{1} **Compare**
and **contrast** permutations and
combinations.

· AII.12_{1} **Compare**
and **contrast** permutations and
combinations.

All.12_{3} **Calculate**
the number of combinations of n objects taken r at a time.

· AII.12_{3} **Calculate**
the number of combinations of *n *objects taken *r *at a time.

All.12_{4} **Use**
permutations and combinations as counting techniques to **solve** real-world problems.

· AII.12_{4} **Use** permutations and combinations as counting techniques to
**solve** practical problems.

· AII.12_{5} **Calculate** and **verify**
permutations and combinations using a graphing utility.

### KEY VOCABULARY

permutation,
combination, Fundamental Counting Principle

*Updated: Oct 27, 2017*