Combinations Finding All Possible Outcomes. What’s for Dessert? For dessert, Sam has a choice of two kinds of pie (apple or peach) and three toppings.

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Presentation transcript:

Combinations Finding All Possible Outcomes

What’s for Dessert? For dessert, Sam has a choice of two kinds of pie (apple or peach) and three toppings (whipped cream, vanilla ice cream, and chocolate ice cream). H How many different desserts are possible?

One way to find all the possible desserts is to make a tree diagram. Sam has two choices of pies: apple peach

On each type of pie, he can put one of three toppings: On each type of pie, he can put one of three toppings: Apple Peach Whipped creamcream

Vanilla Vanilla ice cream ice cream Vanilla Vanilla ice cream ice cream On each type of pie, he can put one of three toppings: On each type of pie, he can put one of three toppings: Apple Peach Whipped creamcream

Vanilla Vanilla ice cream ice cream Vanilla Vanilla ice cream ice cream On each type of pie, he can put one of three toppings: On each type of pie, he can put one of three toppings: Apple Peach Whipped creamcream Chocolate Chocolate ice cream

Vanilla Vanilla ice cream ice cream Vanilla Vanilla ice cream ice cream How many different desserts are possible? How many different desserts are possible? Apple Peach Whipped creamcream Chocolate Chocolate ice cream

What’s My Number? Sue has 4 cards on which one of the digits 2, 8, 5, or 4 is printed. How many different four-digit numbers can she write using each of the digits in each number?

Another way to find all possible combinations is to make an organized list. First list all the ways the numbers could begin…

Then list each possible second digit…

Next list each possible third digit for each pair of numbers in the list…

Last, add the fourth digit to complete the four- digit numbers in the list…

What patterns do you notice? What patterns do you notice? How many different combinations are there with 4 digits? How many different combinations are there with 4 digits? How many with 3 digits? How many with 3 digits?

YOUR TURN! Use a tree diagram or an organized list to show all possible three-letter combinations using the letters A, E, and T. Use a tree diagram or an organized list to show all possible three-letter combinations using the letters A, E, and T. How many three-letter combinations are there? How many three-letter combinations are there? Which combinations form actual words? Which combinations form actual words?