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