A horse race has the following horses running. How many different first, second and third place results are possible: Mushroom Pepper Sausage Tomato Onion.

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Presentation transcript:

A horse race has the following horses running. How many different first, second and third place results are possible: Mushroom Pepper Sausage Tomato Onion Anchovies

A horse race has the following horses running. How many different first, second and third place results are possible: 1st2nd3rd

A restaurant offers the following toppings for their pizzas. How many different 3 topping pizzas could be ordered? Mushroom Pepper Sausage Tomato Onion Anchovies

A restaurant offers the following toppings for their pizzas. How many different 3 topping pizzas could be ordered? Topping MushroomPepperSausage MushroomSausagePepper MushroomSausage PepperSausageMushroom SausageMushroomPepper SausagePepperMushroom

There are 3! combinations of the same three toppings

A restaurant offers a three meal combination package for $ How many different breakfast, lunch, dinner packages are possible? Breakfast 1. Mushroom 2. Pepper 3. Sausage Lunch 1. Ham 2. Tomato Dinner: 1. Onion 2. Olive 3. Anchovies Fundamental Counting Principle

A horse race has the following horses running. How many different first, second and third place results are possible: Mushroom Pepper Sausage Ham Tomato Onion Olive Anchovies Permutation

A restaurant offers the following toppings for their pizzas. How many different 3 topping pizzas could be ordered? Mushroom Pepper Sausage Ham Tomato Onion Olive Anchovies Combination

PermutationsCombinations The number of ways of arranging n items, taken r at a time is: The number of ways of combining n items, taken r at a time is:

Evaluate Each Permutation

Evaluate Each Combination

How many ways can a 5 member club elect a President and Vice President? Systematic Listing of Club Members: Aaron, Bob, Carly, Debbie, Eddie Is this a permutation problem or a combination problem? This is a PERMUTATION problem

How many ways can a 5 member club elect a President and Vice President? Out of 5 members of a club, we are choosing 2 members, one to be President and the other to be VP

How many ways can a 5 member club elect a two person committee? Systematic Listing of Club Members: Aaron, Bob, Carly, Debbie, Eddie Is this a permutation problem or a combination problem? This is a COMBINATION problem

How many ways can a 5 member club elect a two person committee? Out of a 5 member club, we are choosing 2 to be on a committee

How do we determine if a problem is a permutation or a combination? If the order in which items are chosen matters, that is the same items in a different order is a different outcome, then the problem is a PERMUTATION problem

How do we determine if a problem is a permutation or a combination? If the order in which items are chosen DOES NOT matter, that is the same items in a different order is still the same outcome, then the problem is a COMBINATION problem

Is the combination AB the same as BA? Why or why not? AB AC AD AE BA BC BD BE CA CB CD CE DA DB DC DE EA EB EC ED

We could also use a product table to show the possible results. AB AC AD AE BA BC BD BE CA CB CD CE DA DB DC DE EA EB EC ED Vice President President ABCDEABCDE A B C D E

Another option would be to draw a tree diagram. Vice President President BCDEBCDE A B C D E