Question

In a class of 54 students, 18 take bio, 11 take math, 19 take English, 4 take bio and math, 7 take Bio and English, 2 take Math and English and 3 take all 3 classes. How many students do not take any of these classes?

Answer 1

To find the number of students who do not take any of the three classes, we will use the principle of inclusion-exclusion. The total number of students who do not take any of these classes is 8.

Step-by-step explanation:

To find the number of students who do not take any of the three classes, we will use the principle of inclusion-exclusion. We start by adding the number of students who take each individual class: 18 (Bio) + 11 (Math) + 19 (English). However, this counts some students twice because they take more than one class.Next, we subtract the number of students who take two classes: 4 (Bio and Math) + 7 (Bio and English) + 2 (Math and English). Finally, we add back the number of students who take all three classes: 3 (Bio, Math, and English). The total number of students who do not take any of these classes is: 54 - (18 + 11 + 19 - 4 - 7 - 2 + 3) = 54 - 46 = 8.