Of the 400 persons, who were interviewed for a post at an MNC, 200 owned a four-wheeler, 140 owned a debit card and 280 owned a wrist watch. 80 of them owned both, a four-wheeler and a debit card, 60 owned both, a debit card and a wrist watch and 120 owned both, a four-wheeler and wrist watch and 10 owned all three. How many candidates had none of the three objects mentioned?
Answers
Answer:
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your answer is here !
Step-by-step explanation:
=> Number of persons who owned none of the three = Total number of persons - number of persons who owned at least one of three devices.
=> The total number of persons = 400.
Number of candidates who owned at least 1 of the 3 objects = A ∪ B ∪ C,
=> where A is the set of people who owned a four wheeler,
=> B is the set of those who owned a debit card and C is the set of those who owned a wrist watch.
=> As A∪B∪C = A + B + C - {A n B + B n C + C n A} + A n B n C.
=> So, A∪B∪C = 200 + 140 + 280 - {80 + 60 + 120} + 20
=] Or A∪B∪C = 380.
=> 380 candidates who attended the interview had at least one of the three gadgets,
=> so 400 - 380 = 20 candidates had none of three objects.
=> follow me !
Number of persons who owned none of the three =
Total number of persons - number of persons who owned at least one of three devices.
The number of persons = 400.
Number of candidates who owned at least 1 of the 3 objects = A / B / C,
where A is the set of people who owned a four wheeler,
B is the set of those who owned a debit card
C is the set of those who owned a wrist watch.
=> As A/B/C = A + B + C - {A - B + B - C + C -A} + A - B - C.
=> So, A/B/C = 200 + 140 + 280 - {80 + 60 + 120} + 20
=] Or A/B/C = 380.
380 candidates who attended the interview had at least one of the three gadgets,
400 - 380 = 20 candidates had none of these objects.