In a class of 50 students, 30 study Hindi, 25 study English and 11 study both Hindi and English. The number of students who do not study any of these two languages is

Options

A. 11
B. 19
C. 14
D. 6

Answer

To find the number of students who do not study either Hindi or English, we can use the principle of inclusion-exclusion. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Total number of students (N) = 50
- Number of students studying Hindi (H) = 30
- Number of students studying English (E) = 25
- Number of students studying both Hindi and English (H ∩ E) = 11

### Step 2: Use the inclusion-exclusion principle
To find the total number of students studying at least one language (Hindi or English), we can use the formula:
\[ N(H \cup E) = N(H) + N(E) - N(H \cap E) \]
Where:
- \( N(H \cup E) \) is the number of students studying either Hindi or English.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ N(H \cup E) = 30 + 25 - 11 \]

### Step 4: Calculate the total number of students studying at least one language
Calculating the above expression:
\[ N(H \cup E) = 30 + 25 - 11 = 44 \]

### Step 5: Calculate the number of students who do not study any language
To find the number of students who do not study either Hindi or English, we subtract the number of students studying at least one language from the total number of students:
\[ \text{Number of students not studying any language} = N - N(H \cup E) \]
Substituting the values:
\[ \text{Number of students not studying any language} = 50 - 44 = 6 \]

### Final Answer
The number of students who do not study any of these two languages is **6**.

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