Section 9.6: Counting Principles 

Permutation: Use when the order of an event matters. (_nP_r) where n is the number of items and r is the number of items you choose.

Example: When ordering an ice cream cone with two scoops, it matters which flavor you put on the bottom and which one you put on top.  For type of probability, you would use the permutation formula.
If there are 12 favors of ice cream, how many different ways can you scoop two favors on a cone?
The 12 flavors equals the number of items (n) and the two scoops equals the number of items you choose (r).
Plug in the values: ₁₂P₂ = 132 different ways to scoop your ice cream order.

Combination: Use when the order of an event doesn't matter. (_nC_r) where n is the number of items and r is the number of items you choose.

Example: When making a pizza and selecting two toppings, it doesn't matter which topping you put on first.  If you put tomatoes first and then basil or basil first and then tomatoes, the pizza will taste the same.  This is when you use the combination formula.
If there are 8 toppings and you pick two toppings, how many different ways can you make a pizza if each topping is used only once?  The 7 toppings equals the number of items (n) and the two toppings equals the number of items you choose (r).
Plug in the values: ₇C₂ = 21 different types of pizzas.

Combination formula:                                                                                             Permutation formula: 





Letter Counting Example:
How many distinct rearrangements of the letters in the word HAWAIIAN are there? 

(since there are 3 A's and 2 I's you must divide the 8 letters by (3!)(2!)