IGNOU BMTC 103 2026 - From a survey of 120 people, the following data was obtained:90 ow

Question

From a survey of 120 people, the following data was obtained:

90 owned a car, 35 owned a computer, 40 owned a house, 32 owned a car and a house, 21 owned a house and a computer, 26 owned a car and a computer, 17 owned all the three facilities.
i. How many people owned neither of the three.

ii. How many people owned only a car?

iii. How many people owned only a computer?

20 Jan 2026

Answer :

Word Count : 481

Let us solve this step by step using the principle of inclusion-exclusion. Let the sets be: * (C) = people who own a car = 90 * (H) = people who own a house = 40 * (P) = people who own a computer = 35 * (C \cap H) = 32 * (H \cap P) = 21 * (C \cap P) = 26 * (C \cap H \cap P) = 17 i. Number of people who owned neither of the three Using inclusion-exclusion for total owning at least one: [ |C \cup H \cup P| = |C| + |H| + |P| - |C \cap H| - |C \cap P| - |H \cap P| + |C \cap H \cap P| ] Substitute the values: [ |C \cup H \cup P| = 90 + 40 + 35 - 32 - 26 - 21 + 17 ] Step by step: [

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