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,3speed 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 3134 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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View Full Documentstandard 52card deck with flowers on the back and 1 card
drawn from a standard 52card 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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 Spring '08
 BAGCHI

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