Bell work Diagnostic Evaluation Please pick up a Pre-Assessment off the table as you come in to class, take a seat, and get started.

Section 7-1: Permutations and Combinations

Fundamental Counting Principle Definition: If one event can occur in m ways and a second event can occur in n ways, then the number of ways both events can occur is m·n Can this definition be extended to three events? Four events? More?

Examples Lunch Special “Choose 1 of each” Entrée Fried chicken Hamburger Chicken sandwich Side Dish Coleslaw Salad Fries Drink Milk Juice Water Soda How many different meal choices are there?

Most license plates consist of six number and letters. How many different license plates are possible if the six numbers and letters can be anywhere on the license plate? How many would be possible if the license plate number must start with three letters and end with three numbers? What if no letter or number can be repeated?

Permutation Definition: A selection of a group of objects in which order IS important. An ordering of n objects Permutations of n objects: n! = n· (n-1) ·(n-2) ·(n-3) ·... ·(3) ·(2) ·(1) The quantity 0! is defined as 1

Examples A school’s student council is electing new officers. From the total 70 members, only 8 are eligible to run for office. How many different ways are there to fill positions for president, vice president, secretary, and treasurer with eligible members?

How many different phone numbers are possible for the (402) area code? What if there are no restrictions on the area code for a ten-digit phone number?

How many ways can you select 3 people from a group of 7 people? 7 · 6 · 5 = 210 permutations We can also use factorials to find this answer: total arrangements = arrangements of 7 = 7! = 210 arrangements not used arrangements of 4 4! General Formula: n P r = n! = (n – r)!

A bride-to-be has 11 best friends. In how many ways can she select 5 of her best friends to be her bridesmaids? (Assume that the role of maid of honor has already been filled).

Five volunteers? How many different ways can we arrange your classmates in a line? How many different ways can we choose two of them and arrange them in a line?

What happens when not all the objects are distinct? (in other words, some objects repeat). In general, the number of permutations of n objects where one is repeated q1 times, the second is repeated q2 times, and so on, is n! q 1 ·q 2 ·q 3 ·…·q n

In how many ways can you arrange the letters in OHIO? In MISSISSIPPI?

1. You are getting an omelet for breakfast at a hotel restaurant. You have 4 choices of meat, 3 choices of cheese, and 6 choices of vegetables. How many different omelets can you create? 2. How many ways can you listen to 5 songs from a CD that has 14 selections? 3. Which is greater— 7 P 3 or 7 C 4 ? 4. How many different passwords are possible, using four non- repeating letters and two numbers? Make sure you put your name on it and drop your exit slip in the basket on your way out the door. Guided Practice

Textbook pg # 9-13, 31, 32, 37, 38

Talk with your neighbor What is a permutation? Does order matter or not? When would you use this method of counting? Give an example.