1. Combinations Finding All Possible Outcomes

2. 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?

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

4. 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

5. 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

6. 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

7. 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

8. 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?

9. Another way to find all possible combinations is to make an organized list. First list all the ways the numbers could begin… 2 8 5 4

10. Then list each possible second digit…. 28 25 24 82 85 84 52 58 54 42 48 45

11. Next list each possible third digit for each pair of numbers in the list…. 285 258 248 284 254 245 825 852 845 824 854 842 528 582 548 524 584 542 428 482 452 425 485 458

12. Last, add the fourth digit to complete the four- digit numbers in the list…. 2854 2584 2485 2845 2548 2458 8254 8524 8452 8245 8542 8425 5284 5824 5482 5248 5842 5428 4285 4825 4528 4258 4852 4582

13. 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? 2854 2584 2485 2845 2548 2458 2854 2584 2485 2845 2548 2458 8254 8524 8452 8245 8542 8425 8254 8524 8452 8245 8542 8425 5284 5824 5482 5248 5842 5428 5284 5824 5482 5248 5842 5428 4285 4825 4528 4258 4852 4582 4285 4825 4528 4258 4852 4582

14. 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?