1. Factorials How can we arrange 5 students in a line to go to lunch today? _________ __________ __________ __________ ________

2. Factorials Definition: The product of integers from 1 to n. For Example: How many ways can I arrange the letters in the word APRIL?

3. Permutation n is the total and r is the amount chosen An arrangement or listing of objects where order IS important.

4. Permutations ORDER MATTERS!  Placement Examples: assigned seats, winning a race or running a race, 1 st place, 2 nd place, etc  Positions Examples: President, Vice President, Secretary, Treasure  Specific job/chore Examples: Hand out markers, pass out papers, etc

5. Permutations Simplify each expression. a. 12 P 2 b. 10 P 4 c. At a school science fair, ribbons are given for first, second, third, and fourth place, There are 20 exhibits in the fair. How many different arrangements of four winning exhibits are possible? 12 11 = 132 10 9 8 7 = 5,040 = 20 P 4 = 20 19 18 17 = 116,280

6. Permutations Example There are 50 runners in a race. How many different ways can the runners finish in 1 st, 2 nd, or 3 rd ?

7. Permutations Example A president and vice president are being chosen from a group of 20 people. How many ways can this be done?

8. Find Probability There are 10 players on a softball team. Each game the batting order is chosen randomly. Find the probability that you are chosen first & your best friend is chosen second.

9. Combination n is the total and r is the amount chosen A selection of objects where order is NOT important.

10. Combinations A selection of objects in which order is not important. Example: Eight people pair up to do an assignment. How many different pairs are there?

11. Combinations Example How many different ways are there to select two class representatives from a class of 20 students?

12. Combinations Example For your school pictures, you can choose four backgrounds from a list of ten. How many combinations of backgrounds are possible?

13. Find Probability probability There are 28 students in your math class. Your teacher chooses 5 students at random to complete a group project. Find the probability that you and your best friend are chosen to work in the group.

14. Solution The number of possible outcomes The number of favorable outcomes with both of you in it. Probability = 2,600/98,280 = 5/189

16. Permutation or Combination? Mike is picking 4 of his 12 friends to go to the Braves game with him. How many ways can he pick the 4 friends that go with him?

17. Permutation or Combination? How many ways can you arrange 4 of the letters in the word PANTHER?

18. Permutation or Combination? Mr. Wagner needs 3 people from my class of 15 to come help clean up the gym. How many ways can I pick the 3 kids?

19. HW textbook p. 345 #1 – 3, 5 – 7, 25 p. 349 #7 – 10, #17-20