Document Sample

Activator Ice cream activity Counting, Permutations, and Combinations Unit 4 Part 1 Warm Up How many different ways can you arrange the letters in REBEL? How many different ways can you arrange the letters in BERRIEN? Basic (or Fundamental) Counting Principle States that if one event can occur in m ways, and a second event can occur in n ways, then the number of ways that both events can occur is m times n ways. Example: Warm Up Examples (class discussion) Basic (or Fundamental) Counting Principle And…if there is a third event that can occur in p ways, the number of ways that all three events can occur is m times n times p ways. This principle can be extended for any number of events. Graphic Organizer #1 More Basic (or Fundamental) Counting Principle examples… You are asked to create a password for your email account. The password must start with 1 digit (0-9) and be followed by three letters (A-Z). How many different possible passwords are there? number letter letter letter Solution The digit at the beginning has 10 different possibilities (0-9) The second position can be any letter A- Z…26 possibilities The third position can be any letter A- Z….26 possibilities The fourth position can be any letter A- Z…26 possibilities 10 * 26 * 26 * 26 = 175,560 Example 2 Now, let’s try that same password…except none of the letters can be repeated! 10 possibilities 26 possibilities 25 possibilities 24 possibilities 10 * 26 * 25 * 24 = 156,000 Tell the number of possibilities 1. You can go to any of three beaches in 2 choices to make: Choice 1: 3 choices Florida and choose scuba diving, 3 choices Choice 2: of parasailing, or surfing at the beach 9 your 3•3= choice. How many different vacation options do you have? 2. You have 10 shirts, 8 pairs of pants, 3 Choices to make: and 5 pairs of shoes. How many different Choice 1: 10 shirts Choice 2: 8 pants outfit combinations could there be? Choice 3: 5 shoes 10•8•5 = 400 How many different ways can3•2•1 = 6 you rearrange the word CAT? Try HORSE 5•4•3•2•1 = 120 Try HIPPOPOTAMUS 12•11•10•9•8•7•6•5•4•3•2• 1= 479,001,600 Try your name! Complete Counting Principle Practice WS (1-5) Factorials Factorials are indicated by the “!” symbol. Whenever you see a ! with a number that means you multiply the number with every number below it. Ex. 5! Means 5 * 4 * 3 * 2 * 1 = 120 7! Means 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 3! Means 3 * 2 * 1 = 6 0! Always equals 1 Operations with Factorials Factorial practice WS Example: 1! + (6-2)! Example: (7-3)! ÷ 2! Example: 6! ÷ 3! Practice Complete (3-10) What would you do here? How many ways can you choose 3 pictures out of a group of 5 to arrange in a row on your wall? Because we are choosing a group of 3 from a big group of 5…we are not arranging each of the objects…This will take a special formula… Important Questions We are about to learn some formulas. To use these formulas, we need to answer some questions first. How many things are you choosing from? This answer will be your “n” in the formulas. How many things can you choose? This will be your “r” in the formulas. Identify n and r Thirty five people try out for basketball, and only 15 can be on the team. n = 35 r = 15 You can choose three toppings for your pizza. The pizza restaurant now offers 20 different toppings. n = 20 r=3 Does order matter? What if 25 people are running a race, and we want to know how many possibilities there are for the top three finishers. Does order matter? Of course it does! If you get three vegetables on your plate and you get to choose from ten, does order matter? No…you still are going to get each of those three vegetables. Permutations and Combinations Permutations occur when order does matter…like the first three finishers of a race or setting your locker combination or password Combinations occur when order does not matter…like what three vegetables to choose Permutations Use when the order of the items is important, as in a race or arranging things The formula for a permutation is: nPr = __ n!__ (n-r)! Complete graphic organizer #3 on Permutations Practice Using Permutation Formula WS Permutation Practice How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available? What is your “n” value? What is your “r” value? Use the permutation formula to find your answer. More practice… How many different ways can four books be arranged on a shelf if they are selected from eight books? What is your “n” value? What is your “r” value? Use the formula and find the total number of combinations. Combinations Use when items represents different scenarios, such as selecting two types of yogurt from a dairy case from a selection of nine The formula for a combination is: nCr = __ n!__ r!(n-r)! Graphic Organizer #4 Combination example problems You are to select two types of yogurt from the dairy case from a selection of 9. What is your “n” value? What is your “r” value? Use the combination formula to find the number of combinations possible. Another example problem… Select three members from your class to work specific homework problems on the board. What is your “n” value? What is your “r” value? Use the combination formula to find the total number of combinations possible. Complete Combination Practice WS

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 5 |

posted: | 9/1/2011 |

language: | English |

pages: | 30 |

OTHER DOCS BY yaofenji

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.