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Sets, Combinatorics, and Probability
exeRciSeS 4.3
1. All the guests at a dinner party drink coffee or tea; 13 guests drink coffee, 10 drink tea, and 4 drink both
coffee and tea. How many people are guests at the dinner party?
2. In a group of 42 tourists, everyone speaks English or French; there are 35 English speakers and 18 French
speakers. How many speak both English and French?
3. After serving 137 customers, a cafeteria notes at the end of the day that 56 orders of green beans were
sold, 38 orders of beets were sold, and 17 customers purchased both green beans and beets. How many
customers bought neither beans nor beets?
4. A bike show will be held for mountain bikes and road bikes. Of the 24 people who register for the show, 17
will bring road bikes and 5 will bring both road bikes and mountain bikes. How many will bring mountain
bikes?
5. Quality control in a factory pulls 40 parts with paint, packaging, or electronics defects from an assembly
line. Of these, 28 had a paint defect, 17 had a packaging defect, 13 had an electronics defect, 6 had both
paint and packaging defects, 7 had both packaging and electronics defects, and 10 had both paint and
electronics defects. Did any part have all three types of defect?
6. 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 rock, country, and
classical. How many like country?
7. Nineteen different mouthwash products make the following claims: 12 claim to freshen breath, 10 claim
to prevent gingivitis, 11 claim to reduce plaque, 6 claim to both freshen breath and reduce plaque, 5 claim
to both prevent gingivitis and freshen breath, and 5 claim to both prevent gingivitis and reduce plaque.
a. How many products make all three claims?
b. How many products claim to freshen breath but do not claim to reduce plaque?
8. From the 83 students who want to enroll in CS 320, 32 have completed CS 120, 27 have completed
CS 180, and 35 have completed CS 215. Of these, 7 have completed both CS 120 and CS 180, 16 have
completed CS 180 and CS 215, and 3 have completed CS 120 and CS 215. Two students have completed
all three courses. The prerequisite for CS 320 is completion of one of CS 120, CS 180, or CS 215. How
many students are not eligible to enroll?
9. A survey of 150 college students reveals that 83 own automobiles, 97 own bikes, 28 own motorcycles, 53
own a car and a bike, 14 own a car and a motorcycle, 7 own a bike and a motorcycle, and 2 own all three.
a. How many students own a bike and nothing else?
b. How many students do not own any of the three?
10. Among a bank’s 214 customers with checking or savings accounts, 189 have checking accounts, 73 have
regular savings accounts, 114 have money market savings accounts, and 69 have both checking and regular savings accounts. No customer is allowed to have both regular savings and money market savings
accounts.
a. How many customers have both checking and money market savings accounts?
b. How many customers have a checking account but no savings account?
11. At the beginning of this chapter you surveyed the 87 computer users who subscribe to your electronic
newsletter in preparation for the release of your new software product.
The results of your survey reveal that of the 87 subscribers, 68 have a Windows-based system available
to them, 34 have a Linux system available, and 30 have access to a Mac. In addition, 19 have access
to both Windows and Linux systems, 11 have access to both Linux systems and Macs, and 23 can use
both Macs and Windows.
Sets, Combinatorics, and Probability
exeRciSeS 4.3
1. All the guests at a dinner party drink coffee or tea; 13 guests drink coffee, 10 drink tea, and 4 drink both
coffee and tea. How many people are guests at the dinner party?
2. In a group of 42 tourists, everyone speaks English or French; there are 35 English speakers and 18 French
speakers. How many speak both English and French?
3. After serving 137 customers, a cafeteria notes at the end of the day that 56 orders of green beans were
sold, 38 orders of beets were sold, and 17 customers purchased both green beans and beets. How many
customers bought neither beans nor beets?
4. A bike show will be held for mountain bikes and road bikes. Of the 24 people who register for the show, 17
will bring road bikes and 5 will bring both road bikes and mountain bikes. How many will bring mountain
bikes?
5. Quality control in a factory pulls 40 parts with paint, packaging, or electronics defects from an assembly
line. Of these, 28 had a paint defect, 17 had a packaging defect, 13 had an electronics defect, 6 had both
paint and packaging defects, 7 had both packaging and electronics defects, and 10 had both paint and
electronics defects. Did any part have all three types of defect?
6. 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 rock, country, and
classical. How many like country?
7. Nineteen different mouthwash products make the following claims: 12 claim to freshen breath, 10 claim
to prevent gingivitis, 11 claim to reduce plaque, 6 claim to both freshen breath and reduce plaque, 5 claim
to both prevent gingivitis and freshen breath, and 5 claim to both prevent gingivitis and reduce plaque.
a. How many products make all three claims?
b. How many products claim to freshen breath but do not claim to reduce plaque?
8. From the 83 students who want to enroll in CS 320, 32 have completed CS 120, 27 have completed
CS 180, and 35 have completed CS 215. Of these, 7 have completed both CS 120 and CS 180, 16 have
completed CS 180 and CS 215, and 3 have completed CS 120 and CS 215. Two students have completed
all three courses. The prerequisite for CS 320 is completion of one of CS 120, CS 180, or CS 215. How
many students are not eligible to enroll?
9. A survey of 150 college students reveals that 83 own automobiles, 97 own bikes, 28 own motorcycles, 53
own a car and a bike, 14 own a car and a motorcycle, 7 own a bike and a motorcycle, and 2 own all three.
a. How many students own a bike and nothing else?
b. How many students do not own any of the three?
10. Among a bank’s 214 customers with checking or savings accounts, 189 have checking accounts, 73 have
regular savings accounts, 114 have money market savings accounts, and 69 have both checking and regular savings accounts. No customer is allowed to have both regular savings and money market savings
accounts.
a. How many customers have both checking and money market savings accounts?
b. How many customers have a checking account but no savings account?
11. At the beginning of this chapter you surveyed the 87 computer users who subscribe to your electronic
newsletter in preparation for the release of your new software product.
The results of your survey reveal that of the 87 subscribers, 68 have a Windows-based system available
to them, 34 have a Linux system available, and 30 have access to a Mac. In addition, 19 have access
to both Windows and Linux systems, 11 have access to both Linux systems and Macs, and 23 can use
both Macs and Windows.