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A group of friends consists of 12 people who like either football or basketball.

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Question: A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like basketball, how many like both?

Options:

  1. 0
  2. 2
  3. 5
  4. 7

Correct Answer: 2

Solution: 

Using the principle of inclusion-exclusion: Total = Football + Basketball - Both. Thus, 12 = 7 + 5 - Both, leading to Both = 0.

A group of friends consists of 12 people who like either football or basketball.

Practice Questions

Q1
A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like basketball, how many like both?
  1. 0
  2. 2
  3. 5
  4. 7

Questions & Step-by-Step Solutions

A group of friends consists of 12 people who like either football or basketball. If 7 like football and 5 like basketball, how many like both?
  • Step 1: Identify the total number of friends in the group. There are 12 friends.
  • Step 2: Identify how many friends like football. There are 7 friends who like football.
  • Step 3: Identify how many friends like basketball. There are 5 friends who like basketball.
  • Step 4: Use the principle of inclusion-exclusion to find out how many friends like both sports. The formula is: Total = Football + Basketball - Both.
  • Step 5: Substitute the known values into the formula: 12 = 7 + 5 - Both.
  • Step 6: Simplify the equation: 12 = 12 - Both.
  • Step 7: Rearrange the equation to find 'Both': Both = 12 - 12.
  • Step 8: Calculate the result: Both = 0.
  • 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 are the groups of people who like football and basketball.
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