Inclusion-Exclusion Principle
Test your understanding of the Inclusion-Exclusion Principle, a fundamental counting technique in combinatorics.
Questions
In a group of 100 people, 60 speak English, 40 speak Spanish, and 20 speak both English and Spanish. How many people speak neither English nor Spanish?
- 20
- 30
- 40
- 50
A club has 20 members, 10 of whom play tennis, 12 of whom play badminton, and 6 of whom play both tennis and badminton. How many members play neither tennis nor badminton?
- 2
- 4
- 6
- 8
In a survey, 300 people were asked if they liked cats, dogs, or both. 150 people liked cats, 180 people liked dogs, and 60 people liked both cats and dogs. How many people liked neither cats nor dogs?
- 30
- 60
- 90
- 120
A company has 100 employees, 40 of whom work in the sales department, 30 of whom work in the marketing department, and 20 of whom work in both sales and marketing. How many employees work in neither sales nor marketing?
- 10
- 20
- 30
- 40
In a group of 50 students, 25 study math, 20 study science, and 10 study both math and science. How many students study neither math nor science?
- 5
- 10
- 15
- 20
A club has 100 members, 60 of whom are male, 40 of whom are female, and 20 of whom are both male and female. How many members are neither male nor female?
- 0
- 10
- 20
- 30
In a survey, 200 people were asked if they liked coffee, tea, or both. 120 people liked coffee, 80 people liked tea, and 40 people liked both coffee and tea. How many people liked neither coffee nor tea?
- 40
- 60
- 80
- 100
A company has 200 employees, 100 of whom work in the production department, 80 of whom work in the marketing department, and 40 of whom work in both production and marketing. How many employees work in neither production nor marketing?
- 20
- 40
- 60
- 80
In a group of 30 students, 15 study math, 12 study science, and 6 study both math and science. How many students study neither math nor science?
- 3
- 6
- 9
- 12
A club has 40 members, 20 of whom play tennis, 15 of whom play badminton, and 5 of whom play both tennis and badminton. How many members play neither tennis nor badminton?
- 5
- 10
- 15
- 20
In a survey, 100 people were asked if they liked cats, dogs, or both. 60 people liked cats, 50 people liked dogs, and 20 people liked both cats and dogs. How many people liked neither cats nor dogs?
- 10
- 20
- 30
- 40
A company has 150 employees, 75 of whom work in the sales department, 60 of whom work in the marketing department, and 30 of whom work in both sales and marketing. How many employees work in neither sales nor marketing?
- 15
- 30
- 45
- 60
In a group of 40 students, 20 study math, 18 study science, and 8 study both math and science. How many students study neither math nor science?
- 4
- 8
- 12
- 16
A club has 30 members, 15 of whom play tennis, 12 of whom play badminton, and 6 of whom play both tennis and badminton. How many members play neither tennis nor badminton?
- 3
- 6
- 9
- 12
In a survey, 250 people were asked if they liked coffee, tea, or both. 150 people liked coffee, 120 people liked tea, and 60 people liked both coffee and tea. How many people liked neither coffee nor tea?
- 10
- 20
- 30
- 40