Question: In a class of 40 students, 20 play football, 24 play cricket, and 9 play both cricket and football. How many students play neither football nor cricket? How many play cricket but not football? Explain in detail.

Solution:

To find the number of students who play neither football nor cricket, we need to subtract the total number of students who play football and cricket from the total number of students in the class.

1. Total number of students:
40

2. Number of students who play football:
20

3. Number of students who play cricket:
24

4. Number of students who play both cricket and football:
9

5. Number of students who play neither football nor cricket:
To find this, we need to subtract the number of students who play both cricket and football from the total number of students.

Number of students who play neither football nor cricket = Total number of students - Number of students who play football - Number of students who play cricket + Number of students who play both cricket and football

Number of students who play neither football nor cricket = 40 - 20 - 24 + 9

Number of students who play neither football nor cricket = 25

So, 25 students play neither football nor cricket.

6. Number of students who play cricket but not football:
To find this, we need to subtract the number of students who play both cricket and football from the total number of students who play cricket.

Number of students who play cricket but not football = Number of students who play cricket - Number of students who play both cricket and football

Number of students who play cricket but not football = 24 - 9

Number of students who play cricket but not football = 15

So, 15 students play cricket but not football.

Summary:
- The number of students who play neither football nor cricket is 25.
- The number of students who play cricket but not football is 15.