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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.

In a town of 10,000 families, it was found that 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, and 2% buy all three newspapers. Find the number of families which buy only A.

Learn how to apply the Inclusion-Exclusion Principle to calculate the number of families that buy only newspaper A in a town of 10,000 families. Understand key set theory concepts, percentages, and overlapping sets in this detailed problem-solving example.

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