12-6 Counting Principle and Permutations Goals: Use the fundamental counting principle to count the number of ways an event can happen. Use permutations to count the number of ways an event can happen.

Think about going to a Deli 4 meats: ham, turkey, bologna, roast beef 3 cheeses: American, provolone, Swiss 3 breads: white, wheat, rye How many different sandwiches could be made? To answer the question, we could: List all of the options… Use a tree diagram… Use the Fundamental Counting Principle

Turkey & American on white Turkey & American on wheat Turkey & American on rye Turkey & provolone on white Turkey & provolone on wheat Turkey & provolone on rye Turkey & Swiss on white Turkey & Swiss on wheat Turkey & Swiss on rye Roast Beef & American on white Roast Beef & American on wheat Roast Beef & American on rye Roast Beef & provolone on white Roast Beef & provolone on wheat Roast Beef & provolone on rye Roast Beef & Swiss on white Roast Beef & Swiss on wheat Roast Beef & Swiss on rye Ham & American on white Ham & American on wheat Ham & American on rye Ham & provolone on white Ham & provolone on wheat Ham & provolone on rye Ham & Swiss on white Ham & Swiss on wheat Ham & Swiss on rye Bologna & American on white Bologna & American on wheat Bologna & American on rye Bologna & provolone on white Bologna & provolone on wheat Bologna & provolone on rye Bologna & Swiss on white Bologna & Swiss on wheat Bologna & Swiss on rye

Turkey American White Wheat Rye Provolone Swiss Ham American White Bologna American White Wheat Rye Provolone Swiss Roast Beef American White Wheat Rye Provolone Swiss

Vocabulary Fundamental Counting Principle – to find the number of ways a series of events can happen you just have to multiply the possibilities together. Deli example: 4 meats: ham, turkey, bologna, roast beef 3 cheeses: American, provolone, Swiss 3 breads: white, wheat, rye 4 * 3 * 3 = 36

Examples Course Selection: 2 Math, 2 Science, 3 Social Studies, 4 English Police Sketch Artist: 195 hairlines, 99 eyes, 89 noses, 105 mouths, 74 chins License Plates: 3 letters and 2 digits Password: 6 letters and 1 digit 48 choices 13,349,986,650 choices 1,757,600 choices 3,089,157,760 choices

Vocabulary Factorial: Examples: On Calculator: MATH  PRB  ! Used to multiply numbers when you are multiplying an integer times every integer smaller than it. Symbol: ! Examples: 3! 7! On Calculator: MATH  PRB  ! = 3 * 2 * 1 = 6 = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

Examples 6! How many ways can you arrange the letters of SMILE ? How many ways can you arrange the letters of GRADES? How many ways can you arrange the letters of EQUATIONS? = 720 = 60,480 5! = 120 6! = 720 9! = 362,880

Jaime, Shana, Otis, Abigail, and Ernesto are lining up to take a picture on the beach. How many different ways can they line up next to each other? A. 100 B. 240 C. 60 D. 120

Vocabulary Permutations: The number of ways objects can be put in order. Symbol: nPr OR P(n,r) Formula: n is the total number of items (bigger #) r is the number being put in order (smaller #) On Calculator: MATH  PRB  nPr

Examples How many ways could I arrange the seats in this classroom? How many ways could we choose a President, Vice President, Treasurer and Secretary? You are going to visit 6 out of 10 colleges. How many orders could you visit them? 12 skiers are in a competition. How many ways could there be first, second and third place winners? 151,200 1,320

The addresses of the houses on Bridget’s street each have four digits and no digit is used more than once. If each address is made up from the digits 0–9, how many different addresses are possible? A. 24 B. 210 C. 5040 D. 151,200

Practice Worksheet – “12-6 Fundamental Counting Principle and Permutations”

Homework Page P36 #12,13,20 Pages 789-790 #1,11-15,28,29