A group of friends consists of 10 people. If 6 like football, 4 like basketball,

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Question: A group of friends consists of 10 people. If 6 like football, 4 like basketball, and 2 like both, how many like neither sport?

Options:

Correct Answer: 6

Solution:

Using the inclusion-exclusion principle: Total liking at least one sport = 6 + 4 - 2 = 8. Therefore, those liking neither = 10 - 8 = 2.

A group of friends consists of 10 people. If 6 like football, 4 like basketball, and 2 like both, how many like neither sport?

A group of friends consists of 10 people. If 6 like football, 4 like basketball, and 2 like both, how many like neither sport?

Step 1: Identify the total number of friends in the group. There are 10 people.
Step 2: Identify how many people like football. 6 people like football.
Step 3: Identify how many people like basketball. 4 people like basketball.
Step 4: Identify how many people like both sports. 2 people like both football and basketball.
Step 5: Use the inclusion-exclusion principle to find the total number of people who like at least one sport. This is calculated as: (Number who like football) + (Number who like basketball) - (Number who like both) = 6 + 4 - 2.
Step 6: Calculate the total who like at least one sport: 6 + 4 - 2 = 8.
Step 7: To find out how many people like neither sport, subtract the number of people who like at least one sport from the total number of friends: 10 - 8.
Step 8: Calculate the number of people who like neither sport: 10 - 8 = 2.

Inclusion-Exclusion Principle – A method used to calculate the size of the union of multiple sets by including the sizes of the individual sets and excluding the sizes of their intersections.
Set Theory – The study of collections of objects, which in this case involves determining how many individuals belong to different groups based on their preferences.