in a colony 275 families buy tamil newspaper 150 families buy english newspaper 45 families buy hindi newspaper 125 families buy tamil and english newspapers 17 families buy english and hindi newspapers 5 families buy tamil and hindi newspapers and 3 families buy all the three newspapers. if each family buy atleast one of these newspapers then find number of families buy only one newspaper
Answers
Number of families buy Tamil newspaper= A = 275
Number of families buy English newspaper= B = 150
Number of families buy Hindi newspaper= C = 45
Number of families buy both Tamil and English newspaper= A∩B = 125 i.e. AB = 125-3= 122
Number of families buy both English and Hindi newspaper= B∩C = 17 i.e. BC = 17-3= 14
Number of families buy both Tamil and Hindi newspaper= A∩C = 5 i.e. AC= 5-3=2
Number of families buy all three newspapers= ABC = 3
We have to find the number of families who buy only one newspaper = D. According to the Venn diagram,
n(D)= n(A)+n(B)+n(C)-2*[n(AB)-n(BC)-n(AC)}-3*n(ABC)
= 275+150+45-2*[122+14+2]-3*3
= 470-276-9
= 185
Answer: 185 families buy only one newspaper.
Tamil newspaper = 275
English newspaper = 150
Hindi newspaper = 45
Tamil and English newspapers = 125
Hindi and English newspapers = 17
Tamil and Hindi newspapers= 5
Tamil, Hindi and English newspapers = 3
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All 3 newspapers = 3 (depicted in green in the diagram)
Find those that buy 2 newspapers: (depicted in red in the diagram)
Only Tamil and Hindi newspapers = 5 - 3 = 2
Only Hindi and English newspapers = 17 - 3 = 14
Only Tamil and English newspapers = 125 - 3 = 122
Find those that buy only 1 newspaper: (depicted in blue in the diagram)
Only Tamil newspapers = 275 - 122 - 3 - 2 = 148
Only English newspapers = 150 - 122 - 14 - 3 = 11
Only Hindi newspapers = 45 - 14 - 3 - 2 = 26
Total = 148 + 11 + 26 = 185
Answer: 185 families buy only 1 newspaper
