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HW 3 P 569 (11-14, 19) OBJ: Review story problems using venn diagrams

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11. In an election-day survey of 100 voters leaving the polls, 52 said they voted for Proposition 1 and 38 said they voted for Proposition 2. If 18 said they voted for both How many voted for neither? 100 (52) Pr1 Pr2(38) 18 34 20 100 – 52 – 20 28 voted for neither ( ) Pr1 Pr2( ) (52) Pr1 Pr2(38) 18

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12. Although the weather was perfect for the beach party, 17 of the 30 people attending got a sunburn and 25 people were bitten by mosquitoes. If 12 people were bitten and sunburned How many had neither affliction? 30 (17) Sb Msq(25) 12 5 13 30 –17 –13 0 had neither affliction ( ) Sb Msq ( ) (17) Sb Msq(25) 12

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13. In a survey of 48 high school students, 20 liked classical music, 16 liked bluegrass music, Twenty students said they didn’t like either. How many liked classical but not bluegrass? 48 20 + 16 + 20 – 48 8 liked both 48 (20) Cl Bg(16) 8 12 liked classical but 20 not bluegrass ( ) Cl Bg( ) (20) Cl Bg(16) 20

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14. Of the 52 teachers at Roosevelt High School, 27 said they like to go sailing, 25 said they liked to go fishing and 12 said they don’t enjoy either recreation How many enjoy fishing but not sailing? 52 27 + 25 + 12 – 52 12 liked both (27) sail fish (25) 12 13 like fishing 12 but not sailing ( ) sail fish ( ) (27) sail fish (25) 12

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19. In a parking lot containing 85 cars, there are 45 cars with automatic transmissions, 43 cars with rear-wheel drive, and 46 cars with four-cylinder engines. Of the cars with automatic transmissions, 26 also have rear-wheel drive. Of the cars with rear-wheel drive, 29 also have four-cylinder engines. Of the cars with four-cylinder engines, 27 also have automatic transmissions. There are 21 with all three features.

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85 Automatic ( ) Rear-wheel ( ) Automatic (45) Rear-wheel (43) 21 Four-cylinder ( ) Four-cylinder (46)

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85 Automatic (45) Rear-wheel (43) 5 21 6 8 Four-cylinder (46)

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85 Automatic (45) Rear-wheel (43) 5 6 21 8 13 9 11 Four-cylinder (46) b. 85 – (45 + 28) = 85 – 73 = 12 a. How many don’t have auto & rear-wheel but have 4-cyl? 11 b. How many don’t have any of the features? 85 - 45 - 11 - 8 - 9=12

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Permutations n P r & Combinations n C r 10 students each submit a woodworking project into an industrial arts competition. There are to be 1 st, 2 nd, 3 rd, & honorable mention. In how many ways can these awards be made? ___ ___ ___ ___ 1 st 2 nd 3 rd HM 10 _9 _8 _7_ = 5040 n P r = n!_ 10 P 4 = 10!_ = 10! (n-r)! (10-4)! 6! 10 9 8 7 6! 6! In how many ways can a host-couple choose 4 couples to invite for dinner from a group of 10 couples? 10 _9 _8 _7_ 4 _3 _2 _1_ n C r = n!__ 10 C 4 = 10!__ (n-r)! r! (10-4)! 4! 10!__ = 10 9 8 7 6! = 6! 4! 6! 4 3 2 1 5040 = 24 210

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Permutations n P r & Combinations n C r = n! = n!__ (n-r)! (n-r)! r! HW 8 Class Exercises 1 – 4 1. 5 P 2 = 5! 5! 543! (5-2)! 3! 3! 20 2. 6 P 3 = 6! 6! 6543! (6-3)! 3! 3! 120 3. 10 P 3 = 10! 10! 10987! (10-3)! 7! 7! 720 4. 4 P 4 = 4! 4! 4321 (4-4)! 0! 1 24 1. 5 C 2 = 5! 5! 543! (5-2)! 2! 3! 2! 3! 2 10 2. 6 C 3 = 6! 6! 6543! (6-3)! 3! 3! 3! 3! 32 20 3. 10 C 3 = 10! 10! 10987! (10-3)! 3! 7! 3! 7! 32 120 4. 4 C 4 = 4! 4! 4!__ (4-4)! 4! 0! 4! 14! 1

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