Question

In a class of 80 students, 40 bring their textbooks to class, 20 bring some sort of beverage to class, 60 bring calculators to class, while 5 students bring nothing to class. If 30 students bring both their textbooks and calculators to class, how many students bring only a beverage to class.

Answer 1

is it probabilty question or of permutation
i think it is permutation question

Answer 2

Let the event 'bring a textbook' be T, let the event 'bring a beverage' be B and let the event 'bring a calculator' be C.
P(T) = 0.5
P(B) = 0.25
P(C) = 0.75
\[\large P(T\cap C)=0.375\]
\[\large(P \cup C)=P(T)+P(C)-P(T\cap C)=0.5+0.75-0.375=\frac{7}{8}\]
Therefore the number of students who bring either a textbook or a calculator to class is:
\[\large 80\times\frac{7}{8}=70\]
It is given that 5 students bring nothing to class. Therefore the number of students who bring only a beverage to class is:
\[\large 80-70-5=5\]