Question

A university offers 3 calculus classes: Math 2A, 2B and 2C. In both parts, you are given data about a group of students who have all taken at least one of the three classes. (a) Group A contains 157 students. Of these, 51 students in Group A have taken Math 2A, 80 have taken Math 2B, and 70 have taken Math 2C. 15 have taken both Math 2A and 2B, 20 have taken both Math 2A and 2C, and 13 have taken both Math 2B and 2C. How many students in Group A have taken all three classes?

Answer 1

Answer:

4 students

Step-by-step explanation:

The total number of students is given by:

$|A|+|B|+|C|-|A\cap B|-|A\cap C|-|B\cap C| + |A\cap B \cap C| = N$

Where N is the total number of students, A is the number of students that have taken Math 2A, B is the number of students that have taken Math 2B, and C is the number of students that have taken Math 2C:

$|A|+|B|+|C|-|A\cap B|-|A\cap C|-|B\cap C| + |A\cap B \cap C| = N\\51+80+70-15-20-13 + |A\cap B \cap C| = 157\\ |A\cap B \cap C| =4$

4 students in Group A have taken all three classes.

*The number of students that have taken two classes has be subtracted so those students do not get counted twice