We are given a problem where:

• There are 10,000 families in total.
• 40% buy newspaper A.
• 20% buy newspaper B.
• 10% buy newspaper C.
• 5% buy both A and B.
• 3% buy both B and C.
• 4% buy both A and C.
• 2% buy all three newspapers (A, B, and C).

We need to find the number of families that buy only newspaper A.

Let's define:

• Total families = 10,000
• Families buying A = 40% of 10,000 = 4000
• Families buying B = 20% of 10,000 = 2000
• Families buying C = 10% of 10,000 = 1000
• Families buying both A and B = 5% of 10,000 = 500
• Families buying both B and C = 3% of 10,000 = 300
• Families buying both A and C = 4% of 10,000 = 400
• Families buying all three (A, B, and C) = 2% of 10,000 = 200

We will apply the inclusion-exclusion principle to calculate the number of families that buy only A.

Steps:

1. Families buying A and B but not C = Families buying A and B - Families buying A, B, and C
2. Families buying B and C but not A = Families buying B and C - Families buying A, B, and C
3. Families buying A and C but not B = Families buying A and C - Families buying A, B, and C
4. Families buying only A = Total families buying A - (Families buying A and B but not C + Families buying A and C but not B + Families buying A, B, and C)

I will now calculate this.The number of families that buy only newspaper A is 3300.

Would you like more details on any of the steps?

Here are 5 related questions to explore:

1. How would the inclusion-exclusion principle work for more complex sets?
2. What is the role of Venn diagrams in understanding overlapping sets?
3. How would the solution change if the percentages for newspapers B or C were different?
4. Can the inclusion-exclusion principle be applied to more than three sets?
5. How would we calculate the number of families that buy exactly two newspapers?

Tip: When dealing with overlapping sets, breaking them into mutually exclusive parts using the inclusion-exclusion principle simplifies the counting.