By using a Venn diagram and the principle of inclusion-exclusion, we find that 13 students are not in any of the three elective classes (art, music, drama) surveyed among 92 students.
To determine how many students are not in any of the three classes (art, music, drama), we can use a Venn diagram and the principle of inclusion-exclusion.
Let's denote A as the number of students taking art, M as the number of students taking music, and D as the number of students taking drama.
The principle dictates that the total number of students taking at least one class is equal to the sum of the individual groups minus the sum of the pairwise intersections plus the number of students in all three groups.
A = 50 students
M = 35 students
D = 40 students
A ∩ M (Art and Music) = 20 students
M ∩ D (Music and Drama) = 24 students
A ∩ D (Art and Drama) = 19 students
A ∩ M ∩ D (All three classes) = 17 students
Using the formula:
Total in at least one class = A + M + D - (A ∩ M) - (M ∩ D) - (A ∩ D) + (A ∩ M ∩ D)
Total in at least one class = 50 + 35 + 40 - 20 - 24 - 19 + 17 = 79 students
Since there are 92 students surveyed and 79 are in at least one class:
Students not in any class = Total surveyed - Total in at least one class
Students not in any class = 92 - 79 = 13 students
Therefore, 13 students are not in any of the three elective classes.