In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Explanation

To solve the problem, we will use the principle of inclusion-exclusion for sets. Let's denote:

- \( n(C) \): the number of people who like coffee = 37
- \( n(T) \): the number of people who like tea = 52
- \( n(C \cup T) \): the number of people who like at least one of the drinks = 70
- \( n(C \cap T) \): the number of people who like both coffee and tea (this is what we need to find).

According to the principle of inclusion-exclusion, we have:
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