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  • 1. April 12, 20129.6 CountingPrinciplesEssential Question:How do you count the number of ways in which an eventcan occur?Objectives:- Solve simple counting problems- Use the Fundamental Counting Principle- Use permutations and combinations to solve countingproblems. 1
  • 2. April 12, 2012The Fundamental CountingPrinciple Determines: If one group has M choices and another group has N choices, the total number of choices is: 2
  • 3. April 12, 2012Keep in mind:1)2)3) 3
  • 4. April 12, 2012Using the FCP:Ex. 1) A combination lock will open when the rightchoice of 3 numbers (from 1-30, inclusive) is selected.How many different lock combinations are possible?Ex. 2) In a certain state, each automobile licenseplate consists of two letters followed by a four-digitnumber. How many distinct license plate numbers canbe formed? 4
  • 5. April 12, 2012Ex. 3) Problems 1-4 on a quiz are multiple choice (A-E)and problems 5 and 6 are true/false. How many wayscan the quiz be answered? 5
  • 6. April 12, 2012 Combination or Permutation?Combination: Order _________ formula:Permutation: Order _________ formula: 6
  • 7. April 12, 2012Ex. 4) How many ways can eight children line up in a row?The number of permutations of"n" elements is: 7
  • 8. April 12, 2012Eight horses are racing at the Belmont Stakes.Ex. 5) How many different ways can all the horses finish?Ex. 6) How many ways can the horses finish 1st, 2nd, or3rd?Ex. 7) How many ways can a horse finish in the top 3? 8
  • 9. April 12, 2012Ex. 8) A high school baseball team has 15 players. If twoplayers are selected to be co-captains, how manydifferent ways can the co-captains be chosen?Ex. 9) A 5-person dodge ball team is to be made up of 3teachers and 2 students. If 6 teachers and 10 studentsvolunteer to be on the team, how many different teamsare possible? 9
  • 10. April 12, 2012Distinguishable PermutationsHow many different combinations arepossible with 3 letters?Write the possible arrangements of MAT.Write the possible arrangements of MOM. 10
  • 11. April 12, 2012Calculating DistinguishablePermutations 11
  • 12. April 12, 2012Ex. 10) Find the number of distinguishable permutations ofthe group of letters in MISSISSIPPI 12
  • 13. April 12, 2012Assignment:9.6 p. 698 #11-27 (odd), 37-43(odd), 47, 49, 53Quiz #5 on MondayGrading Period Ends (so Moodle!) 13