Answer:
34 students appreciate just two of the activities.
Step-by-step breakdown:
The number of students who enjoy video games is A = 38
The count of students fond of movies is B = 12
The students who thrive on solving math problems is C = 24
A∩B∩C = 8
Using the formula:
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
= 38 + 12 + 24 - n(A∩B) - n(B∩C) - n(A∩C) + 8
Moreover, the count of students that enjoy exclusively one activity can be derived from the following equation:
n(A) - n(A∩B) - n(A∩C) + n(A∩B∩C) + n(B) - n(A∩B) - n(B∩C) + n(A∩B∩C) + n(C) - n(C∩B) - n(A∩C) + n(A∩B∩C) = 30
n(A) + n(B) + n(C) - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 3·n(A∩B∩C) = 30
38 + 12 + 24 - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 24 = 30
- 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) = -68
Thus, n(A∩B) + n(B∩C) + n(A∩C) = 34.
Consequently, the total of students who enjoy just two of the activities equals 34.
