5) The records of 100 SNHU students show the following courses taken: 53 students took History 41 students took Marketing 48 students took Writing 18 students took History and Marketing 21 students took Marketing and Writing 7 students took all 3 courses 9 students took none of these courses Answer the following questions. Show how you obtained your solution. a) How many students took Marketing and Writing, but not History? b) How many students took only History?.

a) How many students took Marketing and Writing, but not History?

14 Students.

b) How many students took only History?

23 Students.

Step-by-step explanation:

We were given the following values in the question

Total number of students = 100

53 students took History = n (H)

41 students took Marketing = n (M)

48 students took Writing = n (W)

18 students took History and Marketing = n (H n M)

21 students took Marketing and Writing = n (M n W)

7 students took all 3 courses = n (H n M n W)

9 students took none of these courses

a) How many students took Marketing and Writing, but not History?

This is calculated as

= n (M n W) - n (H n M n W)

= 21 - 7

= 14

Therefore, only 14 Students took Marketing and Writing but not History.

b) How many students took only History?

Step 1

Subtract the Total number of students from the number of students who did not take any course

100 - 9 = 91 students

Step 2

The number of students who took History and Writing (H n W) was not given, so we find it.

Therefore,

n (H) + n (M) + n (W) - n (H n M) - n (M n W) - n (H n W) + n (H n M n W) = 91

53 + 41 + 48 - 18 - 21 - n (H n W) + 7 = 91

n (H n W) = 149 - 39 - 91

n (H n W) = 149 - 130

n (H n W) = 19

Step 3

To find the number of students taking History only, we calculate it as

Number of Students that took History only = n (H) - n (H n W) - n (H n M) + n (H n M n W)

= 53 - 19 - 18 + 7

= 53 + 7 - 19 - 18

= 60 - 37

= 23

Therefore, the number of students that took only History is 23 Students.