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12-6 Counting Principle and Permutations

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

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12-6 Counting Principle and Permutations

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  1. 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.

  2. 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

  3. 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 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

  4. 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

  5. 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

  6. Vocabulary • Factorial: • 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

  7. Examples = 720 • 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? = 60,480 5! = 120 6! = 720 9! = 362,880

  8. 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

  9. Vocabulary • Permutations: • The number of ways objects can be put in order. • Symbol: nPrOR 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

  10. 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

  11. 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

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

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

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