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. Find how many students take ATMOST TWO OF THESE THREE DRINKS?
Answers
Answer:20
Step-by-step explanation:
is the number of students who had Milk(M) only;
is the number of students who had Tea(T) only;
is the number of students who had Coffee(C) only;
is the number of students who had Milk(M)&Coffee(C) but no Tea(T);
is the number of students who had Milk(M)&Tea(T) but no Coffee(C);
is the number of students who had Tea(T)&Coffee(C) but no Milk(M);
is the number of students who had all the three drinks Milk(M), Coffee(C), Tea(T).
To find the number of students who did not take any of the drink we have to take away students
who take any of the drink from 100 students.
Students who take any of the drink:
= 12, = 5, = 8.
= 10.
= 20 − = 20 − 10 = 10.
= 25 − = 25 − 10 = 15.
= 30 − = 30 − 10 = 20.
Number of students who take any of the drink= + + + + + + =
= 12 + 5 + 8 + 10 + 15 + 20 + 10 = 80.
Number of students who did not take any of the drink= 100 − 80 = 20.
Answer:
80 students take ATMOST TWO OF THESE THREE DRINKS
Step-by-step explanation:
M∩C∩T = 10
M∩C = 20
C∩T = 30
M∩T = 25
M only = 12
C only = 5
T only = 8
MUCUT = M only + C only + T only + M∩C + C∩T + M∩T - M∩C∩T
= 12 + 5 + 8 + 20 + 30 + 25 - 10
= 90
90 students who take atleast any drink
10 students are there who take all drinks
so
Students who take ATMOST TWO OF THESE THREE DRINKS = MUCUT - M∩C∩T
= 90 - 10
= 80
80 students take ATMOST TWO OF THESE THREE DRINKS