1. Chapter 7: Probability Lesson 4: Permutations Mrs. Parziale

2. Vocabulary: Permutations: ORDER ___________! Each _______________________ of a set of objects is called a _______________. MATTERS different arrangement permutation

3. Example 1: If there are ten high school teams in a given conference. How many different possible standings could result (assuming no ties)? __ __ __ __ __ __ __ __ __ __ = ______

4. Permutation Theorem: There are Extra Example: How many different arrangements can be formed using 5 unique vases. N! permutations of n different elements.

5. Example 2: Permutations of n objects taken r at a time. In the conference from a previous example, assume that 4 teams make it to the playoffs. How many ways can this happen? In other words: how many possible groups of _____ can be selected from this group of _____. 1 st Place2 nd Place3 rd Place4 th Place

6. Theorems: Formula for - Permutations of n objects taken r at a time --- The number of permutations of n objects taken r at a time is: “n pick r,” is written n P r Alternate formula for : n P r = n (n – 1) (n – 2) … (n – r + 1)

7. Example 3: EQUATIONS How many different four letter words can be selected from the word EQUATIONS (the words do not need to make sense, and cannot have repeated letters.) Note: if all n objects are selected, then the alternate formula yields:

8. Zero Factorial Definition: 0! = 1 Proof:

9. More Examples: 1. In a 4 person relay race, the fastest runner is typically the last person to run for the relay team. If that place is set, how many different orders are there for the other runners?

10. More Examples: 2. How many different ways can the letters of each word be arranged? a. FLORIDAb. STUDYc. PARALLEL

11. Closure More Examples: 3. Given: Solve for n.

12. Closure More Examples: 4. Given: Solve for n.