Discrete Math

Question

There are 100 students majoring in engineering. There are three math classes offered to the

engineering student's this semester: Calculus, Discrete Math, and Statistics. 28 students take the

Calculus class, and 38 students take Discrete Math. 10 students take both the Statistics and the Discrete

Math class, while 8 take Discrete Math and Calculus. Meanwhile, 15 students take just Calculus. No

students takes all three classes, and 18 of them take none of the classes. Answer the following questions

1.How many students take only the Discrete math class.

 

2.How many students take Discrete Math or Calculus

 

3.How many students only take Statistics?

 

4.Draw a complete Venn Diagram showing how many students are enrolled in each course and

combination of courses.

 

 

Answer 1

The easiest way to do this problem is to do part 4 first, and then use the completed Venn diagram to answer questions 1-3.  

 

Draw a large circle to represent your universe of 100 engineering students.  Inside this circle draw 3 intersecting circles and label them C for Calculus, D for Discrete Math, and S for Statistics.  Now start putting numbers inside the circles to represent the number of students in each combination of courses - 

 

No student takes all three classes, so there is a 0 in the intersection of all 3 circles.  

 

10 students take both Statistics and Discrete Math, so there is a 10 in the intersection of the S and D circles.  

 

8 take Discrete Math and Calculus, so there is an 8 in the intersection of the D and C circles.  

 

15 students take just Calculus, so there is a 15 in the part of the C circle that does not intersect the S or D circles.  

 

28 students take Calculus.  We already have 0 in the intersection of all 3 circles, 8 in the intersection of the D and C circles, and 15 in just the C circle.  So there must be 5 in the intersection of the C and S circles.  

 

38 students take Discrete Math.  We already have 0 in the intersection of all 3 circles, 10 in the intersection of the S and D circles, and 8 in the intersection of the D and C circles.  So there must be 20 in the D circle alone.  

 

18 students take none of the classes, so there is an 18 outside of all 3 of the C, D and S circles (but inside the original large circle).  

 

We have now filled in all of the possible combinations except for Statistics alone.  The numbers we have entered so far (0, 10, 8, 15, 5, 20, and 18) add up to 76, so the remaining 24 students must be in the S circle alone.