Answer:
a) How many students took Marketing and Writing, but not History?
14 Students.
b) How many students took only History?
23 Students.
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.