This problem can be solved using the principle of inclusion-exclusion. Let us define:

• Total number of students: $n = 37$
• Students who like computers: $C = 17$
• Students who like painting: $P = 25$
• Students who like neither: $N = 3$
• Students who like both: $x$ (we need to find this)

Step 1: Calculate students who like at least one activity

Since 3 students like neither activity, the number of students who like at least one activity is: $37 - 3 = 34$

Step 2: Use the inclusion-exclusion principle

The total number of students who like at least one activity is given by: $|C \cup P| = |C| + |P| - |C \cap P|$ Substitute the known values: $34 = 17 + 25 - x$

Step 3: Solve for $x$

$34 = 42 - x \implies x = 42 - 34 = 8$

Final Answer:

The number of students who like both painting and computer is 8.

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Would you like further clarification on this solution?

Here are 5 related questions to deepen your understanding:

1. How would the answer change if the number of students who liked neither was different?
2. What is the total number of students who like only painting?
3. What is the total number of students who like only computers?
4. Can this problem be solved using a Venn diagram? How?
5. How is the principle of inclusion-exclusion useful in other scenarios?

Tip: Always verify your results by plugging values back into the equations to check consistency.