Aim: How many different ways???

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May 14th Aim: How many different ways??? Get Ready: Some books are laid on a desk. Two are English, three are mathematics, one is French, and four are global. Theresa selects an English book and Isabelle then selects a global book. Both girls take their selections to the library to read. If Truman then selects two books at random, what is the probability that he selects an English book or a mathematics book? 1

Factorials 6!= 6 * 5 * 4 * 3 * 2 *1 = 720 12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 *1 = 479,001,600 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040 4! = 8! = 72! = 2

How Many Different Ways??? With your partner, take four different colored blocks and complete the activity to see how many different ways you can answer each situation. We will come back together at. 3

Mr. Rogers is having a contest for his students who are taking the Integrated Algebra Regents Exam. From everyone who takes the exam, he will randomly select only three students from whoever gets a 95+ on the test to take them out for ice cream and give them a free movie pass. After the exam results come in, Jamie got a 96, Adam got a 96, Trevor got a 97, and Alisa got a 99. Since Mr. Rogers said he can only take 3 students, how many different combinations of students (Jamie, Adam, Trevor, and Alisa) can Mr. Rogers take for ice cream and give a free movie pass? Combinations When arranging n objects into r places when order is not important. ncr = npr r! n: the # of objects you're arranging r: the # of places in your arrangement 8C3 = npr = 8*7*6 = 336 = 56 r! 3*2*1 6 Back to Mr. Rogers... n = r = How to do it on the graphing calculator... Practice: 10C5 = 7C2 = 67C21 = The student council has 6 members, but there is going to be a meeting where only 3 members need to attend. How many different triplets can attend the meeting? There are 14 members on a school's basketball team. In how many ways can the coach pick the starters? (There are 5 starters) 4

Stuart is having a race with his four toy cars. He has a blue car, green car, red car, and yellow car that he will release from the top of a ramp that he made. How many different results can Stuart have for which car got in first, second, and third place? Permutations npr = When arranging n objects into r places when order is important. n! (n r)! n: the # of objects you're arranging r: the # of places in your arrangement Back to Stuart n = r = How to do it on the graphing calculator... The shortcut 9P4 =9*8*7*6 = 3024 12P3 =12 * 11 * 10 = 1320 Do you see it? 8P3 = Practice 10P5 = 15P8 = A class of 21 students elects 4 people to office, a president, a vice president, a secretary and a treasurer. How many different ways can people be elected? If 7 people are in a race, then how many different ways of 1st, 2nd, and 3rd place winners can we have? 5

6

Recap Key Points Next Class: Due Next Time: 7

1. How many different 4 digit numbers can you make from the numbers 2, 5, 8, 3? 2. A lock combination has 5 digits between 0 and 9. How many different combinations are there? 3. Sally has 10 posters, but only wants to hang up 3 of themhow many different ways can she choose the 3? 4. Ten people are running in a race how many different ways can the gold, silver and bronze medals be given out? 5. In how many ways can a boss choose 4 out of his 10 employees to be on a committee? 8

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