Answer:
The answer is below
Step-by-step explanation:
Let B represent those that like badminton, F represent those that like football and V represent those that like volleyball. Let x represent the total number of people.
n(B) = (1/3)x, n(F) = (3/4)x, n(V) = (5/6)x
n(B∩F∩V) = 20% of x = 0.2x
n(B∩F) = 17, hence n(B∩F∩V') = 17 - 0.2x
n(V∩F) = 60, hence n(B'∩F∩V) = 60 - 0.2x
n(B∩V) = 65, hence n(B∩F'∩V) = 65 - 0.2x
n(B∪F∪V)' = 8
n(B∩F'∩V') = (1/3)x - 0.2x - (17 - 0.2x) - (65 - 0.2x) = 0.533x - 82
n(B'∩F∩V') = (3/4)x - 0.2x - (17 - 0.2x) - (60 - 0.2x) = 0.95x - 77
n(B'∩F'∩V) = (5/6)x - 0.2x - (60 - 0.2x) - (65 - 0.2x) = 1.033x - 125
Therefore:
x = n(B∩F'∩V') + n(B'∩F∩V') + n(B'∩F'∩V) + n(B∩F∩V) + n(B∩F∩V') + n(B'∩F∩V) + n(B∩F'∩V) + n(B∪F∪V)'
x = (0.533x - 82) + (0.95x - 77) + (1.033x - 125) + (0.2x) + (17 - 0.2x) + (60 - 0.2x) + (65 - 0.2x) + 8
x = 2.1166x - 134
1.1166x = 134
x = 120
Therefore there was 120 students
