Today in Algebra 2? Turn in graded worksheet Notes: Permutations and Combinations –NEED A GRAPHING CALCULATOR Homework

Picking One How many sundaes are possible if you can only choose one from each of the following categories? ice cream flavors: chocolate, vanilla, strawberry, rocky road sauce: hot fudge, caramel toppings: cherries, whipped cream, sprinkles (4)(2)(3) = 24 different sundaes

Repeating Events A test consists of 8 multiple choice questions. How many ways can the 8 questions be answered if each question has 4 possible answers? (4)(4)(4)(4)(4)(4)(4)(4) = 4 8 = 65,536

Permutations An arrangement of objects in a specific order or selecting all of the objects. The number of permutations of n objects taken r at a time, denoted P(n,r) or nPr, is

Example There are ten drivers in a race. How many outcomes of first, second, and third place are possible? Calculator steps: type in number of objects selecting from (bigger number) then press MATH scroll to PRB and select nPr then type in number of objects selected and ENTER (screen should be 10 nPr 3) 720 ways

Example There are 30 students in the Art Club, how many ways can the club select the President, Vice President, and Secretary for the club? 30 P 3 = 24,360 ways

Combinations An arrangement of objects in which order does not matter. Difference between permutations and combinations: –Combinations: grouping of objects –Permutation: putting objects in specific places or positions, or selecting all of the objects.

Permutations vs Combinations Select a committee of 5 people from a group of 33 people. –Combination (order doesn’t matter) Elect a President, Vice President, Treasurer, & Secretary from a group of 40 people. –Permutation (putting in specific places) Pick your favorite soda, and your second favorite soda from a group of 8 sodas. –Permutation (putting in specific places) Buy 3 types of soda at Giant from a group of 30 sodas. –Combination (order doesn’t matter) Arrange the entire set of 12 books on a shelf. –Permutation (arranging all the objects)

Example In a study hall of 20 students, the teacher can send only 6 to the library. How many ways can the teacher send 6 students? Calculator steps same as permutations except select nCr (screen should be: 20 nCr 6) 38,760 ways

Example Jessie is at the library and wants to sign out 8 books but she can only sign out 3. How many ways can she choose which books to sign out? = 56 ways