Explanation:

We need to find the number of people who are 'dancers' AND 'musicians' BUT NOT 'actors'. \nLet's identify the regions based on the diagram: - Rectangle represents Dancers. - Circle represents Musicians. - Triangle represents Actors. 1. First, identify the region representing 'dancers' (Rectangle): The numbers within the rectangle are $\{5, 9, 12, 8, 6, 4, 11, 7\}$. 2. Next, identify the region representing 'musicians' (Circle): The numbers within the circle are $\{10, 9, 12, 8, 6, 11, 7\}$. 3. Find the intersection of Dancers and Musicians (numbers common to both Rectangle and Circle): $\{9, 12, 8, 6, 11, 7\}$. These are the dancers who are also musicians. 4. Finally, exclude those who are 'actors' (numbers within the Triangle): The numbers within the triangle are $\{3, 9, 12, 4, 11\}$. \nFrom the intersection $\{9, 12, 8, 6, 11, 7\}$, we remove any numbers that are also in the Triangle. The common numbers are $\{9, 12, 11\}$. \nSo, the numbers representing dancers who are musicians but not actors are $\{8, 6, 7\}$. \nTo find the total count, sum these numbers: $8 + 6 + 7 = 21$. \nAnalyzing the options: (1) 21: This is the sum of the numbers in the region representing dancers and musicians but not actors. This is correct. (2) 12: This number represents individuals who are actors, musicians, and dancers (intersection of all three shapes). This is incorrect. (3) 16: This is not a direct sum of any specific region for the given condition. This is incorrect. (4) 17: This is not a direct sum of any specific region for the given condition. This is incorrect.