In a class of 50 students, 30 study Basic, 25 study Pascal and 10 study both How many study neither?

Options

A. 15
B. 0
C. 5
D. 35

Answer

To solve the problem, we will use the principle of inclusion-exclusion to find the number of students who study either Basic or Pascal, and then we will determine how many students study neither of the two subjects.

### Step-by-Step Solution:

1. **Identify the Total Number of Students:**
- Total students = 50

2. **Identify the Number of Students Studying Each Subject:**
- Students studying Basic (A) = 30
- Students studying Pascal (B) = 25
- Students studying both subjects (A ∩ B) = 10

3. **Use the Inclusion-Exclusion Principle:**
- According to the principle, the number of students studying either Basic or Pascal (A ∪ B) is given by:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
- Substituting the values:
\[ n(A \cup B) = 30 + 25 - 10 \]
- Calculate:
\[ n(A \cup B) = 55 - 10 = 45 \]

4. **Calculate the Number of Students Studying Neither Subject:**
- To find the number of students studying neither Basic nor Pascal, we subtract the number of students studying either subject from the total number of students:
\[ \text{Students studying neither} = \text{Total students} - n(A \cup B) \]
- Substituting the values:
\[ \text{Students studying neither} = 50 - 45 \]
- Calculate:
\[ \text{Students studying neither} = 5 \]

5. **Conclusion:**
- Therefore, the number of students who study neither Basic nor Pascal is **5**.