Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:
Explanation:
17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.
∴ 8 volunteers are involved in ER alone.
∴ 4 volunteers are involved in all the three projects.
Let x people be involved in FR alone.
∴ Number of people involved in FR and ER but not TR = x – 4
Now, a + b + 4 = 10
∴ a + b = 6
Also, 7 + a + b + 4 + x + x – 4 + 8 = 37
∴ 2x = 16 or x = 8
Number of Volunteers involved in FR > Number of Volunteers involved in TR
And Number of Volunteers involved in FR > Number of Volunteers involved in ER
∴ 16 + a > 17 and 16 + a > 16 + b or a > b
∴ a and b can be (6, 0), (5, 1), (4, 2)
The minimum number of volunteers involved in both FR and TR projects, but not in the ER Project = minimum value of a = 4
Hence, option (c).
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