1. Honors Analysis

4.  Independent Events: Events that do not affect each other  Sample Space: List of all possible outcomes  Fundamental Counting Principle: If events are independent, the number of ways both can occur is the product of the number possible outcomes for each event.  Permutation: An arrangement in which ORDER MATTERS

5.  In how many unique orders can 5 people sit in a row of chairs?  In how many orders can the letters of the word “pencil” be arranged?  In how many ways can five people place first, second, and third in a race?

7.  The goal: Find the number of possible arrangements in the word MISSISSIPPI

8.  Calculate the following factorial values: 0! = 1! = 2! = 3! = 4! = 5! = 6! = 7! =

9. Determine the number of unique arrangements created by the following sets of letters and complete the chart: Do you notice any patterns? **Hint: Factorials! No Repeats2 Same Letters3 Same Letters 3 Letterscowbee- 4 Lettershorntreeepee 5 Lettersangleigloocheese

10.  How many arrangements could be created from the letters in “cheese” if only the e’s can be moved and are distinct from each other (try using e 1 e 2 e 3 ) C H __ __ S __ How might this help you develop a formula?

11.  In how many orders can you sit 3 people around a table? (Careful – no “beginning point”)  4 people?  5 people?  Do you notice a pattern?

12. The chart below shows information about Math Club members: In how many ways could a boy OR girl be selected? In how many ways could a sophomore OR a girl be selected? If order matters, in how many ways could two boys be selected? (A boy AND a boy)

13.  Events are mutually exclusive if one excludes the other from happening. n(A or B) = n(A) + n(B)  If events are non-mutually exclusive, be careful to subtract the number of ways the events can overlap! n(A or B) = n(A) + n(B) – n(A ∩ B)  Multiple Dependent Events: n(A and B) = n(A) · n(B | A), where n(B | A) is the number of ways event B can occur after A occurs