An investigator interviewed 100 students to determine their preferences for the three drinks milk coffee and tea. He reported the following, 10 students had all the three drinks, 20 had milk and coffee, 30 had coffee and tea , 25 had milk and tea, 12 had milk only. 5 had coffee only, 8 had tea only. The number of students that did not take any of the three drinks is.

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Solution

According to given information, the venn diagram is below.
Now, $n (M \cup C \cup T) = 12 + 5 + 8 + 10 + 15 + 20 + 10 = 80$
Now, number of people who did not took any of the drinks is $n (M^{'} \cap C^{'} \cap T^{'}) = n (M \cup C \cup T)^{'}$
$\Rightarrow n (M \cup C \cup T)^{'} = N - n (M \cup C \cup T)$
$\Rightarrow n (M \cup C \cup T)^{'} = 100 - 80 = 20$

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Q. An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee, and tea. The investigator report that 10 students take all three drinks, 20 had milk and coffee, 30 had coffee and tea; 25 students take milk and tea; 12 students take milk only; 5 students take coffee only and 8 students take tea only. Then the number of students who did not take any of three drink is

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(M)

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10

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;

20

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T

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12

had

M

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5

had

C

only;

8

had

T

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An investigator interviewed $100$ students to determine the performance of three drinks : milk, coffee and tea. The investigator reported that $10$ students take all three drink milk, coffee and tea ; $20$ students take milk and coffee; $25$ students take milk and tea ; $20$ students take coffee and tea; $12$ students take milk only; $5$ students take coffee only and $8$ students take tea only. Then the number of students who did not take any of three drinks is