Question

Out of 260 students in a class of a school, 135
like tea, 110 like coffee and 80 like milk, 35 of
these like both tea and coffee, 30 like both tea
and milk, 20 like both coffee and milk. Also,
each student likes atleast one of the three
drinks. How many students like all the three
drinks?​

Answer 1

Step-by-step explanation:

In a group of 50 people 30 like drinking tea and 20 like drinking coffee. How many people like to drink only coffee, if all 50 people liked at least one of the beverages and 6 people like neither tea nor coffee?

Let’s solve this using a venn diagram.

T = Tea

C = Coffee

n means number

n(T) = 30

n(C) = 20

Universal = 50

n(T U C)' = 6 , T union C complement (people who like to drink neither)

Let n(T Π C) i.e. T intersection C (People who like to drink both) = x

n(T) + n(C) - n(T Π C) + n(T U C)' = 50

30 + 20 - x + 6 = 50

56 - x = 50

- x = 50 - 56

-x = -6

x = 6

Therefore people who like to drink BOTH Tea and Coffee are 6.

People who drink coffee = 20

Thus, People who ONLY drink coffee = 20 - 6 = 14 people

I've attached an image with diagram below for better understanding.

Answer 2

Answer:

35+30+20=85

Step-by-step explanation:

85 students like all the three drinks.

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