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ABS No ABS Accident 3 12

Transform this table into a probability table first. ABS No ABS Accident 3 12 No Accid 40 45. ABS. No ABS. Accident. Accident. 3. 12. 12. 15. 15. No Accident. 40. 45. 85. 85. 43. 43. 57. 100. 57. 100.

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ABS No ABS Accident 3 12

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  1. Transform this table into a probability table first. ABS No ABS Accident 3 12 No Accid 40 45 ABS No ABS Accident Accident 3 12 12 15 15 No Accident 40 45 85 85 43 43 57 100 57 100 Questions: 6) Given that the car does not have ABS, what is the prob that it has been involved in an accident? Accident and No ABS 12 4 P(acci|No ABS) = = = Total No ABS 57 19

  2. Counting Principle 2. How many ways can six prizes be awarded to 6 children (assuming each child only gets one prize)? 6*5*4*3*2*1 = 6! 6! = 720

  3. Counting Principle 2. How many ways can six prizes be awarded to 6 children (assuming each prize can be awarded to any of the 6 children)? 6*6*6*6*6*6 = 66 66 = 46,656

  4. Try some on your own: a. 11! 22! 18! =(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1) = 39,916,800 = 175,560

  5. Permutation Rule Taking n objects in a specific order using r objects at a time Symbol: nPr Formula: ___n!___ ((n-r)!) nPr =

  6. Combination A selection of distinct objects without regard to order *ORDER does NOT matter

  7. Combination Rule Symbol: nCr Formula: ___n!___ ((n-r)!r!) nCr =

  8. Combination Rule ___n!___ ((n-r)!r!) Using : nCr = Find the following: 1. 13C8 2. 9C7 ___13!___ ((13-8)!8!) ___9!___ ((9-7)!7!) 1,287 36

  9. Combination Rule Example 1 A bicycle shop owner has 12 mountain bicycles in the showroom. The owner wishes to select 5 of them to display at a bicycle show. How many different ways can a group of 5 be selected? Is there any significance to the order of the 5 bicycles selected? NO! This is why it is a COMBINATION n= 12 possible bicycles r = choosing 5 bicycles

  10. Combination Rule Example 1 A bicycle shop owner has 12 mountain bicycles in the showroom. The owner wishes to select 5 of them to display at a bicycle show. How many different ways can a group of 5 be selected? ___12!___ ((12-5)!5!) nCr = 12C5 = 792 =

  11. Combination Rule Example 2 All of the 15 students in a class draw pictures. Only 9 can be displayed at a time. How many different groups of pictures are possible? Is there any significance to the order of the 9 pictures selected? NO! This is why it is a COMBINATION n= 15 possible pictures r = choosing 9 pictures

  12. Combination Rule Example 2 All of the 15 students in a class draw pictures. Only 9 can be displayed at a time. How many different groups of pictures are possible? ___15!___ ((15-9)!9!) nCr = 15C9 = 5,005 =

  13. Combination or Permutation? 1. A teacher has 5 chores to be assigned to the students each day (sweep, clean board, collect papers, empty trash, pass out books). If there are 18 students in the class, how many possible ways can the 5 chores be assigned? 2. In a club with 12 members, they need 6 members to represent the club at the schools open house. How many ways can they come up with the 6 students?

  14. Combination or Permutation? A teacher has 5 chores to be assigned to the students each day (sweep, clean board, collect papers, empty trash, pass out books). If there are 18 students in the class, how many possible ways can the 5 chores be assigned? Ask yourself, does order matter or are you just choosing 5 students regardless of order? Order matters, therefore it is a PERMUTATION

  15. Combination or Permutation? A teacher has 5 chores to be assigned to the students each day (sweep, clean board, collect papers, empty trash, pass out books). If there are 18 students in the class, how many possible ways can the 5 chores be assigned? Since it is a permutation we use nPr nPr = 18P5 __n!__ ((n-r)!) __18!__ ((18-5)!) _18!_ 13! 1,028,160 18P5 = = = =

  16. Combination or Permutation? In a club with 12 members, they need 6 members to represent the club at the schools open house. How many ways can they come up with the 6 students? Ask yourself, does order matter or are you just choosing 6 members regardless of order? Order does not matter, therefore it is a COMBINATION

  17. Combination or Permutation? In a club with 12 members, they need 6 members to represent the club at the schools open house. How many ways can they come up with the 6 students? Since it is a combination we use nCr nCr = 12C6 __n!__((n-r)!r!) __12!___ ((12-6)!6!) _12!_ 6!6! 924 12C6 = = = =

  18. p211 #1, 5, 8, 10, 13, 18, 23, 24, 28

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