Question

An investigator interviewed 100 students to determine their preferences for the three drinks Milk , Tea and Coffee .He reported the following:10 students had all the three drinks,20 had only Milk and Coffee,30 had Coffee and Tea and 25 had Milk and Tea,12 had only Milk,5 had only Coffee and 8 had only Tea .Find the number of students who do not drink any of these drinks.​

Answer 1

Answer:

According to given information, the venn diagram is below.

Now, n(M∪C∪T)=12+5+8+10+15+20+10=80

Now, number of people who did not took any of the drinks is n(M

′

∩C

′

∩T

′

)=n(M∪C∪T)

′

⇒n(M∪C∪T)

′

=N−n(M∪C∪T)

⇒n(M∪C∪T)

′

=100−80=20