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Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8H 12-2 Counting Outcomes.

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Presentation on theme: "Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8H 12-2 Counting Outcomes."— Presentation transcript:

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2 Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8H 12-2 Counting Outcomes

3 Tree diagrams are a tool used to count the number of possible outcomes in a sample space. A tree diagram starts with one item, then branches into two or more. Those branches each branch into two or more, and so on. The diagram resembles a tree, with a trunk and multiple branches.

4 A one-topping pizza can be ordered with a choice of sausage, pepperoni, or mushrooms, a choice of thin or pan crust, and a choice of medium or large size. Toppings Crust Size Outcomes Sausage Pepperoni Mushrooms thin pan thin pan thin pan medium large medium large medium large medium large medium large medium large STM STL SPM SPL PTM PTL PPM PPL MTM MTL MPM MPL

5 The Redwood coed volleyball team played 3 games against Los Cerritos Middle School. Show the different records the RMS team could have. Game 1 Game 2 Game 3 Outcomes win lose win lose win lose win lose win lose win lose win lose WWW WWL WLW WLL LWW LWL LLW LLL

6 The number of possible outcomes can also be found without constructing a tree diagram. Instead you can use the which takes less time. If an event M can occur in m ways and is followed by an event N that can occur in n ways, then the event M followed by event N can occur in

7 Look at the tree diagram you made for the pizzas. topping choices 3 crust choices 2 size choices 2 # of pizza outcomes 12 Look at the tree diagram you made for the games. win/lose choices 2 win/lose choices 2 win/lose choices 2 # of outcomes 8

8 A sub sandwich restaurant offers four types of sub sandwiches, three different types of potato chips, five types of bread, and six different beverages. How many different sandwich and drink combinations can you order? # sub # chip # bread # beverage # outcomes choices choices You could make a tree diagram to show the number of combinations, but it would take a long time compared to the use of the Fundamental Counting Principle.

9 When Lindsay went on vacation she packed a variety of clothes. How many outfits were possible for her to wear if she could choose one from each of four shirts, three pairs of pants, two pairs of shoes and two jackets? # shirt # pant # shoe # jacket # outfits choices choices choices choices Lindsay could make 48 different outfits to wear from the clothes she packed.

10 Ed and Fred went to an arcade that had 9 different games. In how many different orders can they play the games if the play each one only once? Ed and Fred have nine games to choose from to play first. After choosing a game to play first, there are eight games left to choose from to play second. There would then be seven choices to play third. This process will continue until all the games have been played. There are 362,880 different orders.

11 This is also known as a factorial, written as 9! Factorials are very easy things. Factorials are just products, indicated by an exclamation mark. For example, “six factorial" is written as 6! and means In general, n! means the product of all the whole numbers from n to 1.

12 If Ed and Fred only have enough tokens to play 6 of the 9 different games, how many ways can they do this? There are still 9 choices for the first game, 8 choices for the second game, and so on, down to four choices for the 6 th game.

13 Students at Thousand Oaks HS can choose class rings in one of each of 8 styles, 5 metals, 2 finishes, 14 stones, 7 cuts of stone, 4 tops, 3 printing styles, and 30 inscriptions. How many choices are there for a class ring? If a student narrows the choice to 2 styles, 3 metals, 4 cuts of stone, and 5 inscriptions (and has already made the remaining decisions), how many choices are there for a class ring?

14 In 1963 the US Postal Service instituted the use of five-digit ZIP codes to expedite mail delivery. In a ZIP code, the first digit corresponds to one of 10 national regions. The second and third digits form a number from 01 to 99 that corresponds to a metropolitan area. The last two digits form a number from 01 to 99 that corresponds to an individual post office or zone. How many different 5-digit ZIP codes are possible?

15 How many different outcomes are available for a four- digit number if the first digit must be even, the second digit must be odd, and the third and fourth digits can be anything? How many even digits are there?Four (2, 4, 6, 8) How many odd digits are there?Five (1, 3, 5, 7, 9) How many total digits are there?Ten (0,1,2,3,4,5,6,7,8,9)


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