The survey of a group of students showed that 50 liked tea, 40 liked coffee, 35 liked milk, 20 liked coffee as well as tea, 18 liked tea as well as milk, 12 liked coffee as well as milk and 7 liked all three. If every student liked at least one drink.

How many students were asked this question?

Solution:

Let U be the set of students who were surveyed.

Let T, C and M represent the sets of students who liked tea, coffee, and milk, respectively.

Here,

$n(T) = 50$

$n(C) = 40$

$n(M) = 35$

$n(C \cap T) = 20$

$n(T \cap M) = 18$

$n(C \cap M) = 12$

$n(T \cap C \cap M) = 7$

$n( \overline{T \cup C \cup M})= 0$

To find: n(U) = ?

We know,

$n(U) = n(T \cup C \cup M)$

$= n(T) + n(C) + n(M) - \{ n(C \cap T) + n(T \cap M) + n(C \cap M) \} + n(T \cap C \cap M)$

$= 50 + 40 + 35 - (20+18+12) + 7$

$= 82$

Hence, the required number of total students who were surveyed is 82.

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