1. Warm-Up 4/29

3. Rigor: You will learn how to find the number of possible outcomes using the Fundamental Counting Principle, permutations and combinations. Relevance: You will be able to solve probability problems using the Fundamental Counting Principle, permutations and combinations.

4. 0-4 Counting Techniques

5. Probability is a measure of the chance that a given event will occur. Outcome is the result of a probability experiment or an event. Sample Space is the set of all possible outcomes of an experiment A tree diagram can be used to list all outcomes in a sample space. EX: Blood type R H factor A BABO +–+– +–+– +–+– +–+–

6. Fundamental Counting Principle Words – The number of possible outcomes in a sample space can be determined by multiplying the number of possible outcomes for each event. Symbols – If event M can occur in m ways and is followed by event N that can occur in n ways, then the event M followed by N can occur in m n ways. This rule can be extended for 3 or more events. 4 possible blood types and 2 possible RH factors then there are 4  2 or 8 possible ways to label blood.

7. Example 1: A bicycle manufacturer makes five- and ten-speed bikes in seven different colors and four different sizes. How many different bikes do they make? & 4 frame choices 7 color choices,2 gear choices, 56 different bicycles can be made.

8. When there are m ways to do one thing, and n ways to do another, then there are m n ways of doing both.

9. Your Turn: You are picking out an outfit. There are 3 pants and 2 shirts. How many possible outfits? (draw a tree diagram) 3 2 = 6 outfits 1 231 23 abab abab abab

10. Permutation is an arrangement of a group of distinct objects in a certain ORDER. There are 6 permutations of the letters A, B and C. ABC, ACB, BAC, BCA, CAB, CBA _______  _________  ________ = choices for first letter choices for second letter choices for third letter total number of permutations 3 2 1 = 6 permutations 3 2 1 = 3!

12. Example 2a: There are 8 finalists in a band competition. How many different ways can the bands be ranked if they cannot receive the same ranking? The bands can be ranked in 40,320 different ways.

13. Example 2b: How many different ways are their to order 16 pool balls? What if we don't want to choose them all, just 3 of them?

14. Example 2c: How many different ways are their to unlock the lock? In the lock, there are 10 numbers to choose from (0,1,...9) There are 1000 permutations to unlock the lock. So, we should really call this a "Permutation Lock"! There are 3 numbers.

15. Your Turn: 1.You have 5 books to arrange on a shelf. How many different ways can this be done? 2.To create an entry code for a push-button lock, you need to first choose a letter and then, three single- digit numbers. How many different entry code can you create? 3.In how many ways can 25 runners finish first, second and third?

17. Example 3: How many ways can two students be assigned to five tutors if only one student is assigned to each tutor? 5 different tutors taken 2 at a time. The students can be assigned in 20 different ways. n = 5 r = 2

18. Your Turn: A photographer has matted and framed 15 photographs and needs to select 10 for a show. How many ways can the photographs be arranged?

19. In English we use the word "combination" loosely My fruit salad is a combination of apples, grapes and bananas The combination to the safe was 472 –We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad. –Now we do care about the order. "724" would not work, nor would "247". It has to be exactly 4-7-2

20. Star This If the order doesn't matter, it is a Combination. If the order does matter it is a Permutation. To help you to remember, think “Combination”… Committee “Permutation”... Position

22. Example 4: How many ways are there to chose 5 cards from a standard deck of 52 playing cards? 52 cards taken 5 at a time and order doesn’t matter. There are 2,598,960 ways to choose 5 cards from a standard deck of playing cards. n = 52 r = 5 210

23. Example 5: Twenty-five students write their name on paper. Then three names were picked at random to receive prizes. (permutation or combination) a.Selecting 3 people to each receive a “no homework” pass. b.Selecting 3 students to receive one of the following prizes: 1 st prize – a new graphing calculator; 2 nd prize- a “no homework” pass; 3 rd prize – a new pencil. Order doesn’t matter so this is a combination. Order does matter so this is a permutation.

24. Your Turn: A restaurant offers a total of 8 side dishes. How many different ways can a customer choose 3 side dishes?

25. Assignment Prob/Stats #1 WS, 1-19 All Conics Project Due Dates: Sections 3 & 4 + 1 & 2 due tomorrow YOU MUST HIGHLIGH CORRECTIONS USING A BLUE HIGHLIGHTER.

26. Warm-Up 4/29 1.A folders come in 8 different colors. How many different ways can I choose 4 colors? 2.A push-button lock, has a code that you need to first choose a letter and then, 4 single-digit numbers. How many different entry code can you create? 2

27. Conics Project Due Dates: Sections 3 & 4 + 1 & 2 due tomorrow YOU MUST HIGHLIGH CORRECTIONS USING A BLUE HIGHLIGHTER.