Discrete Math Question??

Question

There are 40 students in their first year of Computer Science program. All of these students must take either Discrete Math or Statistics, or both. There are 28 students in total taking Discrete Math. There are 5 students taking both Discrete Math and Statistics.

 

How many students are only taking Statistics?

Answer 1

Let's call N(D) the number taking Discrete Math and N(S) the number taking statistics.

 

N (D or S) = N(D) + N(S) - N (D and S)

 

Since everyone has to take at least one of the courses N (D or S) = 40.

 

N(D) = 28

N (D and S) = 5

 

So 40 = 28 + N(S) - 5 = 23 + N(S)

 

So N(S) = 17

 

5 of the 17 students taking statistics are taking both classes, so the other 12 are taking only Statistics.  So the answer is 12.