Question

In a group of 500 persons, 300 take tea, 150 take coffee, 250 take cold drinks, 90 take tea and coffee, 110 take tea and cold drinks, 80 take coffee and cold drink, 30 none of them. Find the no. of persons who take all the three drinks.

Answer 1

Let the set of people who take tea =A
set of people who take coffee =B
set of people who take cold drink= C

Acc to ques,

n(A)=300, n(B)=150, n(C)=250

also, n(A n B)=90, n(A n C)=110, n(B n C)=80

30 take none of 3 drinks

Hence, (A u B u C) = 500-30=470
by formula,

n(A u B u C)= n(A)+ n(B) +n(C) - n(A n B ) - n(B n C)- n(A n C)+ n(A n B n C)
470 = 300 + 150 + 250 - 90 - 110 - 80 + n(A n B n C)

n(A n B n C)= 50

Therefore number of people who take all the 3 drinks = 50

Answer : 50