1. Counting Principles 1.What is 7! 7*6*5*4*3*2*1 = 5040 2.Which counting method do you use when order matters, a permutation or a combination? 3.Which is a larger number, or ? 4. What is = 7*6*5 = 210 5. What is=7*6*5/(3*2*1) = 210/6 =35

2. Counting Principles 6.Seven people are in a race. How many ways can they finish 1st, 2nd and 3rd? =7*6*5 = 210 7. How many ways can you choose a team of three people from a group of seven? = 35 8.How many ways can you choose four people from a group of seven? = 35 9. Why are you answers to seven and eight the same? Choosing 3 “winners” from seven is the same as choosing four “losers”

3. Counting Principles You have a Snickers bar, a bag of chips, a Reesy cup, a pack of Nabs and a Moon Pie in your bookbag. You plan to eat one item in each of your next two periods of school. How many ways can you do this? Consider each food different. = 20

4. Counting Principles There are 25 desks in Mr. Gillam’s class and he has 28 students. In how many different ways can they sit at a desk if all desks are filled and three student are left standing ? 5.8 x 10 28 There are 25 desks in Mr. Gillam’s class and he has 28 students. How many different ways can you choose the three students who are left standing? 3276

5. Counting Principles You have to play 10 games of Grand Theft Auto IX: Blythewood to qualify for the tournament next month. You have 20 evenings left to play, and can play one game an evening. How many different schedules for playing the ten games are possible? 184756 You and six other people are in a tournament playing the Guitar Zero video game. How many ways can 1st, second and third place be awarded? 120

6. Counting Principles Bernie Madoff’s answering machine is full with 32 messages. If 32 distinct individuals called him with death threats, how many different orders could the calls have come in? 32! = 2.63 x 10 35

7. Counting Principles Seventy-five AIG employees are receiving bonuses. Five of these bonuses are greater than 4 million dollars. How many ways can you select the five employees to get the five large bonuses from the seventy-five employees. 17259390 If the government chooses three of the five employees in problem number 19 to testify at a congressional hearing, how many permutations of the order of the three testimonies are possible? 60

8. Counting Principles How many different arrangements are there of the letters in the word NERDY if repetition is not allowed? 5*4*3*2*1 = Which of the following is equivalent to n!? a) b) c) d) 42