Question

A group of 570 students were surveyed about the courses they were taking at their college with the following results:

257 students said they were taking Math.
282 students said they were taking English.
323 students said they were taking History.
154 students said they were taking Math and English.
171 students said they were taking Math and History.
143 students said they were taking English and History.
80 students said they were taking all three courses.

How many students took English and History, but not Math

Answer 1

The number of students who took English and History, but not Math is 143.

Explanation:

Denote the subject choices as follows:

M = a students was taking Math

E = a students was taking English

H = a students was taking History

The data provided is as follows:

N (M) = 257

N (E) = 282

N (H) = 323

n (M ∩ E) = 154

n (M ∩ H) = 171

n (E ∩ H) = 143

n (M ∩ E ∩ H) = 80

Consider the Venn diagram below.

From the provided data and the Venn diagram the value of the set E and H minus M is 143.

Thus, the number of students who took English and History, but not Math is 143.