1. 9/21/2015MATH 106, Section 21 Section 2 Tree Diagrams Questions about homework? Submit homework!

2. 9/21/2015MATH 106, Section 22 Using “brute force” to solve problems Some simple problems can be solved using “brute force” List all possible arrangements and count them The hard part – making sure that the list includes each one exactly once Don’t miss any No duplicates You are going to flip a coin three times. How many possible outcomes are there? Let’s list them. Let’s use a tree diagram (a pictorial representation) to get all of the possibilities. HHH HHTHTH THH HTT THTTTH TTT

3. 9/21/2015MATH 106, Section 23 What we mean by a “tree” … A common point called the root The lines are the branches The more parts there are, the taller the tree is We will grow our trees to the right! heads tails 1 st toss heads tails heads tails 2 nd toss heads tails heads tails heads tails heads tails 3 rd toss Let’s do more examples …

4. 9/21/2015MATH 106, Section 24 You have 4 shirts (red, white, blue, and khaki) and 3 pairs of pants (khaki, black, and blue jeans). Construct a tree diagram to find how many different outfits can you make. Does it matter whether you pick shirts first or pants first to build the tree diagram? red khaki shirtspants white blue khaki blue jeans black The number of different outfits is 12. The answer is (of course) the same if we pick pants first to build the tree diagram. #1

5. 9/21/2015MATH 106, Section 25 How many different outfits can you make, if you never have the same color shirt and pants? The number of different outfits without the same color shirt and pants is 12 – 2 = 10.

6. 9/21/2015MATH 106, Section 26 A hot dog cart has the following condiments: ketchup, mustard, and relish. How many different “kinds” of hot dogs can you make? yes no ketchupmustard relish yes no yes no yes no yes no yes no yes no The number of different “kinds” of hot dogs can you make is 8. #2

7. 9/21/2015MATH 106, Section 27 How many different “kinds” of hot dogs can you make with exactly 2 toppings? The number of different “kinds” of hot dogs can you make with exactly 2 toppings is 3.

8. 9/21/2015MATH 106, Section 28 Homework Hints: In Section 2 Homework Problem #8, In Section 2 Homework Problem #9, In Section 2 Homework Problems #11 and #12, don’t be confused or fooled by the way the sentence is worded. Consider “cream” possibilities and “sugar” possibilities separately. consider each topping separately. consider possibilities for die#1 followed by possibilities for die#2 in a tree diagram.