#### Math - 2018-19

# AII.12 - Permutations and Combinations

AII.12The student willcomputeanddistinguishbetween permutations and combinations.

*Adopted: 2016*

### 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.

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

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

· 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.

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

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

· 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: Aug 23, 2018*