Question

In a class of 40 students, 20 took Mathematics, 18 took Statistics, 16 took English, 7 took Mathematics and Statistics, 7 took Mathematics and English, 9 took Statistics and English, and 3 took all the three courses. How many students are not taking any of these courses?​

Answer 1

Answer:

18

Step-by-step explanation:

If 11 people are taking both courses, this means 51-11 or 40 are taking kickboxing only and 25-11 or 14 are taking yoga only. The number of people taking at least one course, therefore, is 40 + 14 + 11 = 65. The 83 members minus the 65 that are taking courses leaves 18 who are not taking any courses

Answer 2

Given:

Total number of students that took mathematics$=20$

Total number of students that took statistics$=18$

Total number of students that took english$=16$

Total number of students that took maths and statistics$=7$

Total number of students that took maths and english$=7$

Total number of students that took statistics and english$=9$

Total number of students that took all three courses$=3$

To find: Total number of students that took none of the courses.

Solution:

Draw the required figure.

Add the individual subject students and subtract the dual subject students and then add the triple subject students that would give us the count of all the students.

Understand that, If that’s more than the number of students then there’s something wrong with the given data. If that’s exactly equal to the number of students then all the students have taken some course(s) or the other. If that’s less than the number of students then subtracting this from the number of students would give us the count of students have not taken any course(s).

Find the count of students having taken some courses or the other.

$\[20 + 18 + 16 - 7 - 7 - 9 + 3 = 57 - 23\]$

                                             $=34$

Subtract the count of students having taken some courses or the other from the total students.

$40-34=6$

Hence, the number of students that took none of the courses is $6.$