Question

In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take both tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes atleast one beverage, find the total number of students in the hostel.

Answer 1

Let T = set of students who take tea

C = set of students who take coffee

M = set of students who take milk

∴ n(T) = 25, n(C)

= 20, n(M)

= 15,

n(T ∩ C) = 10,

n(M ∩ C) = 8,

n(T ∩ M) = 0,

n(T ∩ M ∩ C) = 0

∴ Total number of students in the hostel = n(T ∪ C ∪ M)

= n(T) + n(C) + n(M) – n(T ∩ C) – n(M ∩ C) – n(T ∩ M) + n(T ∩ M ∩ C)

= 25 + 20 + 15 – 10 – 8 – 0 + 0

= 42