In a survey of 100 students, the numbers taking various courses..

Question

In a survey of 100 students, the numbers taking various courses were found to be English, 65; mathematics, 41; chemistry, 52; English and mathematics, 26; English and chemistry, 33; mathematics and chemistry, 34; and courses in all three areas, 20.
(a) How many students were taking mathematics, but neither English nor chemistry?

students

(b) How many were taking mathematics and chemistry, but not English?

students

(c) How many were taking English and chemistry, but not mathematics?

students

Answer 1

First, we start with a venn diagram.

We know that 20 students are enrolled in all three classes. To find how many are taking in both, we substract the courses taken by all three from both.

E and M = 26 - 20 = 6

E and C = 33 - 20 = 13

M and C = 34 - 20 = 14

Now we find the total number of people taking the one subject by subtracting the total of students taking both that course and another course and the number of students taking all three.

For example, let's consider mathematics. We know there are, in total, 41 students are taking the class. We know that 6 students take Math and English and 14 students take Math and Chemistry and 20 students take all three. . To find the total we have:

41 - 6 - 14 - 20 = 1

For English it will be as follows:

65 - 13 - 20 - 6 = 26

For Chemistry, it will be as follows:

52 - 13 - 20 - 14 = 15

Though not accurate, the venn diagram should look similar to this:

E = 65 M = 41

Total in E = 26 Total in M = 1

In both E and M = 6

All Three = 20

In both E and C = 13 In both M and C = 14

Total in C = 15

C = 52

Now we can answer the questions:

1. One student in only taking Mathematics.
2. 14 students were taking only Mathematics and Chemistry.
3. 13 students were taking only English and Chemistry.