In a survey of a group, 60 like tea, 45 like coffee, 30 like milk, 25 like coffee and tea, 20 like milk and tea, 15 like coffee and milk and 10 like all three drinks. Show the information in a Venn-di

• Only Coffee and Tea: $n(C \cap T) - n(C \cap T \cap M) = 25 - 10 = 15$
• Only Milk and Tea: $n(M \cap T) - n(C \cap T \cap M) = 20 - 10 = 10$
• Only Coffee and Milk: $n(C \cap M) - n(C \cap T \cap M) = 15 - 10 = 5$

• Only Tea: $n(T) - [n(C \cap T) - n(C \cap T \cap M)] - [n(M \cap T) - n(C \cap T \cap M)] - n(C \cap T \cap M)$ $n(T) - n(C \cap T) - n(M \cap T) + n(C \cap T \cap M) + n(C \cap T \cap M) - n(C \cap T \cap M)$ $n(T) - n(C \cap T) - n(M \cap T) + n(C \cap T \cap M)$ $60 - 15 - 10 - 10 = 60 - (15+10+10) = 60 - 35 = 25$
• Only Coffee: $n(C) - [n(C \cap T) - n(C \cap T \cap M)] - [n(C \cap M) - n(C \cap T \cap M)] - n(C \cap T \cap M)$ $n(C) - n(C \cap T) - n(C \cap M) + n(C \cap T \cap M)$ $45 - 15 - 5 - 10 = 45 - (15+5+10) = 45 - 30 = 15$
• Only Milk: $n(M) - [n(M \cap T) - n(C \cap T \cap M)] - [n(C \cap M) - n(C \cap T \cap M)] - n(C \cap T \cap M)$ $n(M) - n(M \cap T) - n(C \cap M) + n(C \cap T \cap M)$ $30 - 10 - 5 - 10 = 30 - (10+5+10) = 30 - 25 = 5$

The Venn diagram would show three overlapping circles for Tea (T), Coffee (C), and Milk (M).

• The intersection of all three ($T \cap C \cap M$) is 10.
• The intersection of only $T$ and $C$ is 15.
• The intersection of only $T$ and $M$ is 10.
• The intersection of only $C$ and $M$ is 5.
• The region for only $T$ is 25.
• The region for only $C$ is 15.
• The region for only $M$ is 5.

The total number of people surveyed is the union of all three sets, $n(T \cup C \cup M)$.
Using the Principle of Inclusion-Exclusion:
$n(T \cup C \cup M) = n(T) + n(C) + n(M) - n(T \cap C) - n(T \cap M) - n(C \cap M) + n(T \cap C \cap M)$
$n(T \cup C \cup M) = 60 + 45 + 30 - 25 - 20 - 15 + 10$
$n(T \cup C \cup M) = 135 - 60 + 10$
$n(T \cup C \cup M) = 75 + 10$
$n(T \cup C \cup M) = 85$

Alternatively, sum all the distinct regions from Step 1 and Step 2:
$n(T \cup C \cup M) = (\text{Only T}) + (\text{Only C}) + (\text{Only M}) + (\text{Only T and C}) + (\text{Only T and M}) + (\text{Only C and M}) + (\text{T and C and M})$
$n(T \cup C \cup M) = 25 + 15 + 5 + 15 + 10 + 5 + 10$
$n(T \cup C \cup M) = 85$

The number of people surveyed is $\boxed{\text{85}}$.