To find out how many residents read all three newspapers, we can use the principle of inclusion and exclusion.
Let's define the following variables:
- $n(A)$: Number of residents who read Newspaper A
- $n(B)$: Number of residents who read Newspaper B
- $n(C)$: Number of residents who read Newspaper C
- $n(A cap B)$: Number of residents who read both Newspaper A and Newspaper B
- $n(A cap C)$: Number of residents who read both Newspaper A and Newspaper C
- $n(B cap C)$: Number of residents who read both Newspaper B and Newspaper C
- $n(A cap B cap C)$: Number of residents who read all three newspapers
According to the principle of inclusion and exclusion:
$$n(A cup B cup C) = n(A) + n(B) + n(C) - n(A cap B) - n(A cap C) - n(B cap C) + n(A cap B cap C)$$
Given the information in the question:
- $n(A) = 300$
- $n(B) = 200$
- $n(C) = 150$
- $n(A cap B) = n(A cap C) = n(B cap C) = 0$ (since there are no overlaps mentioned between any two newspapers)
Substitute the values into the formula:
$$500 = 300 + 200 + 150 - 0 - 0 - 0 + n(A cap B cap C)$$
Solving for $n(A cap B cap C)$:
$$n(A cap B cap C) = 500 - 300 - 200 - 150 = 50$$
Therefore, there are 50 residents who read all three newspapers - A, B, and C.
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