SILENTLY Algebra 1 7 Feb 2011 SILENTLY Write down HOMEWORK DUE next class P 2 and P 4: pg. 575: 8, 13- write basic information and show steps use A.B.E. for 13 e P5: pg. 574: 6 write basic info and show steps WARM UP: Make a tree, list and area model showing all possible outcomes. You can take a bus, car, light rail or walk to the mall. You can then take the elevator, stairs or escalator to reach your favorite store on the second floor. Find: a) P( bus and stairs) b) P (light rail)

Objective Students will be able to create models of probability and use the counting principal to determine the number of possible outcomes. Homework Due TODAY pg. 590: 1, 2 write basic information and use A.B.E. Pg. 230: 4 use A.B.E. for part (g) Yesterday’s - Class work Two dice sums- student exemplars

Probability Quiz TUTORING– Mon and Wed, Need to make up quiz: P2: Muse, Classie P4: Karla, Haley, Anis, Tyson P5: Natasha, Jesus COME IN TODAY, PLEASE- lunch or after school.

10.4 Counting Techniques Investigation- PRIZES Each student needs to briefly write what you are doing for each step and writing your answers Will be collected as class work and randomly graded Silently read steps 1 and 2, then summarize them on your paper. Think- pair- share Continue investigation, completing steps 3 Discuss steps 4 and 5 whole class discussion.

words to know permutation - an arrangement in which the order is important. ex: for letters a, b, c, there are the following permuations: abc, acb, bac, bca, cab and cba. (pepperoni and onion is different than onion and pepperoni) combination - an arrangement in which order is unimportant. ex. for letters a, b, c, there are the following combinations: abc (ex. A tossed salad of lettuce, onion and carrots) (pepperoni and onion = onion and pepperoni) You must consider whether or not repetition is allowed.

Counting Principle If there are a ways to make a choice and for each of these, there are b ways to make a second choice, and so on. The product a∙b∙c… is the total number of possible outcomes.

example How many different student identification (ID) numbers can be assigned if an ID number consists of any two letters from the alphabet followed by any three digits? ____∙ ____∙ ____∙ ____∙ ____

what if letters and numbers can not be repeated? How many different student identification (ID) numbers can be assigned if an ID number consists of two letters from the alphabet followed by three digits, and no repetition is allowed? ____∙ ____∙ ____∙ ____∙ ____

practice- think-pair-share how many different ID numbers can be assigned if an ID number consists of any 6 digits and they can be repeated? ____∙____∙____∙____∙____∙____ = How would the total number be different if numbers could not be repeated? ____∙____∙____∙____∙____∙____ =

permutation- example A pg.570 You are redecorating your room and have five pictures to arrange in a row along one wall. The pictures are labeled A, B, C, D and E. 1) how many ways can you arrange the five pictures? There are 5∙4∙3∙2∙1 or 120 different arrangements. 2) How many different ways can you arrange any 3 of the 5 pictures in random order? There are 5∙4∙3 or 60 different arrangements. We can write this in math notation as 5 P 5 = 120 read as “the number of permutations of 5 things chosen 5 at a time” We can write this in math notation as 5 P 3 = 60 read as “the number of permutations of 5 things chosen 3 at a time”

practice The San Benito Boys and Girls Club basketball coach has seven players dressed for a game. a. In how many ways can they be arranged to sit on the bench? b. Five players are assigned to specific positions for the game. How many different teams can the coach put on the floor? c. pg. 575, # 12

example c- pg. 572 A piggy bank contains 6 coins: dollar, half-dollar, quarter, dime, nickel and penny. If you turn it upside down and shake it, one coin will fall out at a time. a) If you shake it until 3 coins come out, how many different sets of coins can you get? This is a combination because the order of the coins in the piggy bank doesn’t matter. It is the same thing to have a nickel, dime and penny in the piggy bank as having a penny, nickel and dime. We can see that there are 6∙5∙4 = 120 possible sets, but DNP = DPN = NDP = NPD = PDN = PND, so we must divide 120 by 6. We can write this in math notation as 6 C 3 = 20 read as“the number of combinations of 6 things chosen 3 at a time” 6 C 3 =

Quiz Do your best! Be respectful to your classmates… silence please. When you are done, turn your quiz over on your desk. You may silently work on your homework.