hw7solutions

hw7solutions - ECE 369 Homework#7 Solutions(Sixth Edition...

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ECE 369 Homework #7 Solutions (Sixth Edition) Section 3.2 ----------- 23) A new car can be ordered with a choice of 10 exterior colors; 7 interior colors;automatic,3-speed or 5 speed transmission; with or without airconditioning; with or without power steering; and with or without the option package that contains the power door lock and the rear window defroster.How many different cars can be ordered? Solution: (10)(7)(3)(2)(2)(2) = 1680 24) In #23, how many different cars can be ordered if the option package comes only on a car with an automatic transmission? Solution: (10)(7)(1)(2)(2)(2) + (10)(7)(2)(2)(2)(1) = 1120 Problems 31-34 concern the set of three digit numbers (between 100 and 999 inclusive) 33) How many are divisible by 4? Solution: (9)(5)(3) //middle digit even,third digit 0,4,8 + (9)(5)(2) //middle digit odd third digit 2 or 6 = 135 + 90 = 225. 34) How many are divisible by 4 or 5? Solution: 225 (numbers divisble by 4) + (9)(5)(1) //middle digit odd,third digit 0 + (9)(10)(1) //third digit 5 = 225 + 45 + 90 = 360 35) How many are divisible by 4 and 5? Solution: (9)(5)(1) //middle digit even,third digit 0 = 45 36) How many are divisible by neither 4 nor 5? Solution: 900 - 360 =540. For #56 and #61, a hand consists of 1 card drawn from a
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standard 52-card deck with flowers on the back and 1 card drawn from a standard 52-card deck with birds on the back. 58) How many hands consist of a pair of aces? Solution: (4)(4) = 16 63) How many hands have a face value of less than 5? Solution: Face value less than 5 can occur in the disjoint ways shown below: flower face value bird face value 1 1,2,or 3 2 1 or 2 3 1 Each has (4)(4) ways of occurring so the total is (6)(16) =96. Section 3.3 ----------- 5) In a group of 24 people who like rock, country, and classical music, 14 like rock, 17 like classical, 11 like both rock and country, 9 like rock and classical, 13 like country and classical and 8 like country, rock and classical. How many like country? Solution: 24 = 14 + 17 + x - 11 - 9 - 13 + 8 //Use the principle of inclusion and exclu$ so x = 18 8) Among a bank's 214 customers with a checkings or savings account, 189 have checkings accounts, 73 have regular savings accounts, 114 have money market savings accounts, and 69 have both checkings and regular savings accounts.
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hw7solutions - ECE 369 Homework#7 Solutions(Sixth Edition...

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