Question:
A particular school management wants to contact all parents, all businessmen and all engineers. The following statistics are available with the school.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people who need to be contacted are _________.
A particular school management wants to contact all parents, all businessmen and all engineers. The following statistics are available with the school.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people who need to be contacted are _________.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people who need to be contacted are _________.
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To find the number of distinct individuals in multiple overlapping sets, use the principle of inclusion-exclusion.
Updated On: Nov 21, 2025
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Correct Answer: 2535
Solution and Explanation
We are given the following sets:
- \( B \) = Businessmen = 50,
- \( E \) = Engineers = 25,
- \( P \) = Parents = 2500.
We are also given the intersections:
- \( B \cap E = 0 \) (No businessmen are engineers),
- \( B \cap P = 25 \) (Businessmen who are parents),
- \( E \cap P = 15 \) (Engineers who are parents).
We are tasked with finding the total number of distinct individuals to contact, which corresponds to the union of the three sets: \[ |B \cup E \cup P| = |B| + |E| + |P| - |B \cap E| - |B \cap P| - |E \cap P| + |B \cap E \cap P|. \] Since no businessmen are engineers, \( B \cap E = 0 \), and thus: \[ |B \cup E \cup P| = 50 + 25 + 2500 - 0 - 25 - 15 + 0 = 2535. \] Thus, the total number of people to contact is \( 2535 \).
- \( B \) = Businessmen = 50,
- \( E \) = Engineers = 25,
- \( P \) = Parents = 2500.
We are also given the intersections:
- \( B \cap E = 0 \) (No businessmen are engineers),
- \( B \cap P = 25 \) (Businessmen who are parents),
- \( E \cap P = 15 \) (Engineers who are parents).
We are tasked with finding the total number of distinct individuals to contact, which corresponds to the union of the three sets: \[ |B \cup E \cup P| = |B| + |E| + |P| - |B \cap E| - |B \cap P| - |E \cap P| + |B \cap E \cap P|. \] Since no businessmen are engineers, \( B \cap E = 0 \), and thus: \[ |B \cup E \cup P| = 50 + 25 + 2500 - 0 - 25 - 15 + 0 = 2535. \] Thus, the total number of people to contact is \( 2535 \).
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