In a department, 24 employees know typing and 11 know stenography, 25 know to use a computer. 7 know both typing and stenography, 4 know stenography and computers, 12 know typing and computers and 3 know all the three. If there were 50 employees in the department, find how many employees don't know none of the three jobs.

Options

A. 40
B. 10
C. 47
D. 33

Explanation

To solve the problem, we will use the principle of inclusion-exclusion and a Venn diagram to find out how many employees do not know any of the three jobs: typing, stenography, and computers.

### Step-by-Step Solution:

1. **Define the Sets**:
- Let \( T \) be the set of employees who know typing.
- Let \( S \) be the set of employees who know stenography.
- Let \( C \) be the set of employees who know computers.

We are given the following information:
- \( |T| = 24 \) (employees know typing)
- \( |S| = 11 \) (employees know stenography)
- \( |C| = 25 \) (employees know computers)
- \( |T \cap S| = 7 \) (employees know both typing and stenography)
- \( |S \cap C| = 4 \) (employees know both stenography and computers)
- \( |T \cap C| = 12 \) (employees know both typing and computers)
- \( |T \cap S \cap C| = 3 \) (employees know all three)

2. **Apply the Inclusion-Exclusion Principle**:
To find the total number of employees who know at least one of the three jobs, we use the formula:
\[ |T \cup S \cup C| = |T| + |S| + |C| - |T \cap S| - |S \cap C| - |T \cap C| + |T \cap S \cap C| \]

Substituting the values:
\[ |T \cup S \cup C| = 24 + 11 + 25 - 7 - 4 - 12 + 3 \]

3. **Calculate the Total**:
\[ |T \cup S \cup C| = 24 + 11 + 25 - 7 - 4 - 12 + 3 = 40 \]

4. **Find Employees Who Don't Know Any of the Jobs**:
We know the total number of employees in the department is 50. To find those who do not know any of the three jobs, we subtract the number of employees who know at least one job from the total number of employees:
\[ \text{Employees who don't know any job} = 50 - |T \cup S \cup C| = 50 - 40 = 10 \]

5. **Final Answer**:
Therefore, the number of employees who do not know any of the three jobs is **10**.